Figure I'd do what I do best and apply my analytical abilities to trying to work out some semblance of a tier list for the melee weapons in GE3. Note that this is based primarily my own experiences, with a bit of input from others on the discord.
In order of frequency of use, I've played Biting Edge, Heavy Moon, Long Blade, Buster Blade, Short Blade, Variant Scythe, Charge Spear, and Boost Hammer. As such, this list may and likely will change as I use the latter few more.
I will be judging weapons on the following categories: overall damage potential (plainly, how much damage the weapon is capable of dealing), utility (things like mobility, auxiliary actions, etc.), Burst Arts (the damage potential and utility of BAs specifically), and survivability (how much proper use of each weapon puts you at risk of taking damage and being knocked out).
I will try my best to eliminate personal bias, but again, this list is based primarily on my own personal use frequency and playstyle, which favors highly aggressive play.
Anyway, without further ado...!
Those who know me knew this would make the top spot. Taking the Short Blade's position as the fastest, shortest-reach weapon, the Biting Edge focuses on staying in the Aragami's face and being constantly on the attack. While its raw stats and damage output are normally quite low, its true merit lies in its Blade Special Action, which combines the two blades and transforms the weapon into Glaive Form, which allows for infinite combos (at the cost of stamina) both on the ground and (with the proper Burst Art) in the air, highly aggressive distance-closing options, boosted damage, and the added feature of increasing damage after attacking for a certain amount of time.
Right off the bat, the biggest downside to this weapon is the Glaive form's stamina drain. There are skills and BCUs (burst control units) that lessen this, but in the end you are going to have to mind your stamina gauge and remember to shift back to dual form when your stamina runs low (alternatively, you could set yourself up for quickened stamina regen when out of breath, or passive stamina regen while attacking in dual form, since Glaive form disables stamina recovery altogether). Ultimately, the trade-off for Glaive form's unmatched damage output is making you far less useful in dual form while waiting for your stamina to recharge. Additionally, the Biting Edge has no weapon options with Crush damage, meaning that your ability to break parts may suffer depending on what you're fighting.
Now, onto the pros of Biting Edge. As stated above, the Glaive form's damage output is, quite literally, unmatched. With the Halo Assault BA, attacking a weak point or a broken weak point even, you can easily deal 300-500 damage per hit at up to 6-8 hits per second. Even when facing a rank 7 Aragami, the battle might as well be over if you can break a part and position yourself at point-blank range with full stamina. You'll be dealing thousands of damage per second, will likely break one or two more parts while the Aragami is downed (due to Glaive form's superior reach, especially with Halo Assault), and if the Aragami doesn't die right then and there, it will likely be only a few hits from death.
Additionally, the Biting Edge offers the best (well, tied with Heavy Moon and Long Blade) aerial offensive option in the game, in the form of the Petal Frenzy BA, which allows you to perform an infinite combo in the air as long as your previous hit connects. You will, however, rise ever so slightly with each hit, meaning that, ultimately, the combo is not TRULY infinite. However, this is nonetheless the best option for dealing damage against Aragami like Ra and False Idols.
Damage Potential: 10/10. Loses points for the necessity of reverting to dual form to recharge stamina, as well as not having the parts breaking potential of other weapons.
Utility: 9/10. The Glaive form's ground triangle attack offers a low-stamina-cost option for closing distances without dropping combos, and the ability to form change in midair offers great utility when fighting floating Aragami.
Burst Arts: 10/10. Halo Assault is the best BA in the game, and Petal Frenzy is a superb aerial option.
Survivability: 6/10. With having to be at point-blank range constantly, coupled with the Glaive form's stamina drain, you'll probably be dying a lot until you get the hang of stamina management and reverting to dual form to retreat.
Heavy Moon is the current meta weapon, and for good reason. It has the heavy damage capabilities of the Buster Blade from previous GE games with the speed of a Short Blade. Additionally, it offers two alternative attacking options: Moon Storm (its Blade Special Action), an infinite swinging combo where each hit strikes multiple times, and Raging Moon, a charged attack that contacts the enemy and deals constant ticks of damage.
The biggest downside to Heavy Moon, and the reason I prefer Biting Edge over it, is the slow recovery times on its animations. Compared to faster weapons like the Biting Edge or Short Blade, the recovery frames on the Heavy Moon's animations are slightly more sluggish, potentially putting you more open to enemy attacks between attacks of your own. Additionally, aside from its air triangle attack, Heavy Moon completely lacks any mid-combo attacking options for closing distance.
However, while not as... demonically powerful as the Biting Edge, the Heavy Moon nonetheless offers superb damage output at far higher survivability. There are four Burst Arts I'd like to highlight: Roaring Axe Combo, Lunar Orbit, Falling Moon, and Moonlight Blade. The first of these, Roaring Axe Combo, is a modifier for the triangle attack finisher of a Moon Storm combo, and adds an extra horizontal swing onto the end. While you cannot cancel between these two swings, the multiple hits per swing combined with th Heavy Moon's crushing damage means that this is EXCELLENT at breaking parts on grounded Aragami. The second, Lunar Orbit, is a standard damage modifier BA for the aerial combo, but the ability to perform sustained aerial combos by canceling with an air devour means that, for certain enemies with parts that can be reached in the air (Ra, False Idols, Sariels, and Megiddo Odin), this is an excellent option for sustained damage—however, it leaves you largely immobile, so watch out for outside attacks. The third, Falling Moon, is the best chase option to combo into from a Dive. It drops you and covers decent horizontal distance, making it suitable for pursuit or for closing the last bit of distance if your Dive falls short. Finally, Moonlight Blade is an oft-overlooked BA due to the infrequency of use of step attacks, but it allows you to combo your step directly into a Raging Moon without the need for a charge, with the added bonus of dealing extra damage to downed enemies. Under that circumstance, you'll be able to easily match a Biting Edge's damage output on a broken part with Halo Assault.
Damage Potential: 9/10. Compared to the Biting Edge, the Heavy Moon has a higher general output at the cost of a lowered specialized output under certain circumstances.
Utility: 8/10. Due to the slower speed and decreased pursuit/connecting options mid-combo, the Heavy Moon loses a point compared to the Biting Edge, but the ability of the air triangle attack to be used as a chase option somewhat makes up for this.
Burst Arts: 10/10. Roaring Axe Combo is among the highest standard damage-dealing BAs in the game, and Moonlight Blade will SHRED downed Aragami if a broken weak point is within reach.
Survivability: 7/10. The slightly longer reach and better pursuit options outside of combos give the Heavy Moon an edge over the Biting Edge, but the slower attacks and sluggish recovery frames leave you more open.
Kept you waiting, didn't I? A surprise entrant in S Tier that I honestly didn't expect, the Long Blade may have lost Tornado Rush and Rising Dragon, but the Burst Arts it gained in exchange more than make up for this.
Right off the bat I will say this: the Long Blade has no downsides. It doesn't have the raw damage output in skilled hands that the Biting Edge does, but in all my time playing the Long Blade with the BA setup I use, I have yet to find any actual downsides. It excels in every area, from pursuit to damage to aggressive utility.
The Burst Arts I highly recommend are Void Cutter for Air and Apsara Wings for Step. Apsara Wings brings to mind the final stage of Rising Dragon from Rage Burst, complete with the damage boost on broken weak spots. With a non-elemental rank 7 Long Blade, I've been able to hit around 2.5k damage with such an attack. Plus, it carries you into the air, allowing a perfect transition to Void Cutter, the bread and butter of every Long Blade. This aerial BA sends you forward with three wide-reaching vertical spins, allowing you to re-angle yourself in-between each one. What this lets you do is not only pursue and chase enemies but also focus all three attacks on a single spot, making it th Long Blade's best option for concentrated aerial damage and parts breaking. Assuming you land all hits on weak spots, a full Apsara Wings --> Void Cutter combo can deal upwards of 4000 damage in only 3-4 seconds, allowing you to reposition yourself for another approach.
Damage Potential: 8/10. The Apsara Wings --> Void Cutter combo doesn't have the raw output potential of Halo Assault or Moonlight Blade, but it has far more utility without putting you as much at risk.
Utility: 9/10. Void Cutter is this weapon's bread and butter, and proper use of it will ensure you are always on the attack.
Burst Arts: 9/10. Again, Void Cutter. This thing is superb at breaking parts due to its three successive attacks coming out so quickly.
Survivability: 8/10. You're slightly vulnerable during the windup to Apsara Wings' slash, but during Void Cutter, either you're moving a lot or you're sufficiently outside of most Aragami's reach, giving you plenty of leeway.
The reigning damage king of the series thus far returns, and while it no longer sits in the throne it used to occupy, the Buster Blade is nonetheless a solid damage dealer with a surprising amount of utility.
Some obvious downsides are its slow startup speed and the delay before its third melee combo hit (a new addition to the weapon that slows down its basic melee combo), as well as a lack of overall variety in viable attacking options. The Long Blade also suffered that last problem, but unlike the Buster Blade, the Long Blade's best set has more than enough viability to make up for it.
However, the Buster Blade is capable of some nasty single hits, which was frankly always its forte. Deadly Glide allows for a powerful aerial pursuit option (allowing you to air devour to continue your attack), and Destruction is a step BA with superarmor that extends your reach when closing distance on the ground. However, most of your damage is likely going to come from Overkill, a Charge Crush modifier that lets you charge up to three stages for a downright obliterative CC hit, capable of dealing up to 10k damage in testing. However, even more so than with regular CC, Overkill REQUIRES the Aragami to be Downed or Held—otherwise, you can guarantee you'll be interrupted. Additionally, Overkill does allow for easy bond breaks if you hit an Aragami right, but to pull this off to its maximum capacity, the Aragami will need to be Downed or Held already, and even then there are other weapons/BAs that can pull off the multiple part break just as well.
Damage Potential: 8/10. The Buster Blade isn't as aggressive as previous entries on this list, but Overkill will guarantee you absolutely slaughter Aragami as soon as they can no longer move.
Utility: 5/10. Aside from Deadly Glide, you don't really have any super viable pursuit options, and the slow speed of the weapon means your combo-chained movement options are few and far between.
Burst Arts: 8/10. Overkill is the highest-damaging single hit in the game, and if you can manage to get off two fully charged Overkills on a downed Aragami's weak spot, it'll probably die.
Survivability: 8/10. Despite the weapon's slow speed, it has a very long reach, meaning that you'll be beyond the reach of many Aragami's more dangerous attacks such as the Havakiri's spin if you attack from far enough away.
As much shit as I give the Short Blade in GE3 (largely due to the Biting Edge stealing its "fastest weapon" niche), it's actually surprisingly useful. While not super impressive in the damage department, it's the single best weapon in terms of utility and survivability, due not only to its capacity for air steps but also its newfound capacity for infinite air steps.
The Short Blade doesn't really have many options for high damage. It retains Blood Cascade and Astral Dive from Rage Burst (under different names, of course), but other than that, most of its BAs are centered around mobility and alterations thereof, adding movement options to various attacks. Aside from the BA that allows your air triangle attack to descend straight down, it doesn't have anything super aggressive, either, aside from the Blood Cascade stand-in, which has the glaring downside of leaving you completely open.
That said, where the Short Blade shines over every other weapon is in its sheer utility. The ability to air step out of harm's way during an aerial combo, and to cancel the air step into another one with an air square attack, means that you will never lose your target even if the Aragami moves around. See an attack coming? Air step away, then air step right back in.
Damage Potential: 5/10. Aside from the Astral Dive stand-in, the Short Blade doesn't really have much of anything going for it.
Utility: 10/10 for the infinite air steps alone.
Burst Arts: 6/10. Again, there's only a small handful of BAs that allow for viable damage options.
Survivability: 10/10. Again, infinite air steps let you distance yourself from an Aragami at a moment's notice.
(Note: From here on out, I have less experience with these weapons. I'll update these entries as I play more with them.)
Retaining much of its same functionality from Rage Burst, the Boost Hammer is still functionally a shorter, more aggressive Buster Blade, with the same upsides and downsides to Boost Ignition, which will be your bread and butter and in which you will be spending most of your time. While offering unparalleled ability to break parts due to its crushing focus, the short reach, awkward handling, and at times aggravating recovery between attacks leaves you a bit more open than I'd like to be. Additionally, much of the utility of Boost Drive as a movement option has been largely superseded by the presence of Dive.
Damage Potential: 7.5/10. Just like in Rage Burst, the Boost Hammer here retains its ability to perform highly aggressive sustained combos. However, it lacks the presence of BAs as viable as Halo Assault or Moonlight Blade, letting it fall off in that department.
Utility: 7/10. Boost Drive is still good for closing distance mid-combo, but if the enemy moves too far away, you'd be better off Diving.
Burst Arts: 7/10. This is where I have the least experience, but from what I've seen, there's nothing here that lets it stand out too much when compared to its Rage Burst incarnation.
Survivability: 5/10. Due to its awkward short reach and stamina drain in Boost Ignition, you have to keep careful watch of your surroundings if you want to stay alive, even more so than with Biting Edge due to its sluggish recovery.
Behaving exactly the same as it did in Rage Burst, the Variant Scythe is actually worse than it used to be. Gone is the multi-hit utility and damage-dealing of Mortal Divide, the bread and butter for many a scythe main—the only saving grace of this weapon in GE3 is that Heaven or Hell, the Execution stand-in, is slightly more forgiving to pull off. Nonetheless, the lack of Extend Bite utility—the loss of it, even—makes this game's incarnation fall compared to its glory days in Rage Burst.
Damage Potential: 6/10. Aside from Execution, this weapon has nothing going for it for competitive, viable damage options.
Utility: 8/10. It still has the longest reach of any melee weapon, but... that's it.
Burst Arts: 6/10. Aside from HoH, again, there are very few BAs that allow this weapon to stand out, aside from perhaps the aerial BA that turns your triangle attack into an extended three-hit vertical spin, which helps with staying aggressive in the air.
Survivability: 6/10. The Variant Scythe has the same problem here that it did in Rage Burst—staying in Extend Bite mode, the only way to deal viable damage, makes you a sitting duck.
Just like in Rage Burst, the Charge Spear remains a mediocre weapon, lacking much in the way of damage or utility potential beyond the BAs focused on Charge Glide. Its Blade Special Action allows the player to perform a backflip, but this is among the worst BSAs in the game, with its only utility being for emergency escapes. Even then, the Short Blade has it beat both in the "emergency escape" regard and in the attack speed regard, and the Long Blade has it beat in terms of weapons with similar reach—to say nothing of the other weapons in S Tier and above. Make no mistake, the Charge Spear isn't a bad weapon in the right hands, but... well, there's nothing that makes it remarkable, just like in Rage Burst.
Damage Potential: 6/10. Unless you're spamming Charge Glide, nothing doing. And god forbid if you drop a combo and lose your Fang Deployment.
Utility: 7/10. Aside from its backflip and the ability of Charge Glide to close distance... nothing.
Burst Arts: 5/10. Nothing here really stood out to me as being able to elevate the usefulness of the weapon beyond its base capabilities—at least not beyond how it was in Rage Burst, and even then it was... mediocre beyond Crescendo and MAYBE Hurricane Period.
Survivability: 6/10. Again, its backflip and Charge Glide give it neat distance control, but the impetus to stay up close so as not to drop a combo and lose your Fang Deployment kind of cancel that out.