I did something like this back when the Japanese version came out, but now that the English version is out (in NA), I figured I'd write up another article where I discuss the different Predator Styles and their comparative effectiveness.
So, without further ado!
Bändiger: Easy S. Lets you close distances like a champ and grants superarmor while dashing. Charge time is a little long, but not enough to be noticeable, and the 100% Burst gauge granted is a definite plus.
The Dragon: Another solid Charge devour. Good not only for its forward reach but also for its sideways and vertical reach. Great for pestering Aragami that are hanging out in the lava in the Infernal Subway and are out of reach of your melee attacks.
Orca: The best PS for multiplayer, hands down. Quick charge time and it puts down a healing cloud for your allies. Plus, there's no limit to how many healing clouds you can have out at once.
Hawk's Flight: Probably the single best utility PS in the game. Closes distances very well and sets you up for an aerial combo or immediate air devour. Plus, lets you pass through enemies if you want something to use for spot dodging.
Mistral: It's only rank 1, but its low cooldown is good for continuing combos, and if your target initiates an attack while you're devouring, you'll be in a position to quickly dodge or guard before the attack hits. Solid, top-tier PS for utility purposes.
Cornix: My favorite PS in the game, easy. Refills more OP the higher up in the air you are, and even the base recovery amount is extremely high. Couple this with Devour Oracle Absorb coming off a double-jump to max altitude, or use immediately off of Hawk's Flight or Downburst, and expect to see a near-complete recovery of a 150-OP OP gauge in a single devour.
Divine Relish: Kind of situational, but if you can sneak up on an Aragami while it's eating or catch them in a trap/inflict Hold with melee attacks/bullets, that's a free level 3 Burst even when you're playing solo. It loses points for its immense charge time, but it's more than good for what it does.
Kagachi: IMO less useful than The Dragon due to its longer charge time, but if you want a compromise between The Dragon's utility and a higher amount of Burst granted, go with this.
Sechshorn: A damn fine PS for Combo. Lets you create distance between you and an Aragami to dodge attacks and reposition yourself for further attacks. Loses points because it doesn't really have much of a niche.
Sturm: The opposite of Sechshorn, and really one of the only three PS you should ever be using on Step. Hell, it makes a good follow-up to Sechshorn if you want to get off a quick 1-2 devour combo with minimal vulnerability.
Guzzle: Combines Sturm and Sechshorn into a single action. Not as good as either of those for comboability, but as its own, single action, it surpasses them easily due to its utility. Really, it all depends on your play style.
Raven: Not as good as Cornix due to its lack of that crazy OP recovery, but still good for maintaining aerial combos. The fact that it's rank 2 increases the variety of CUs you can use with it.
Mist Vane: Best air devour for a purely melee-focused build. Has wide-reaching range, hits below you instead of simply at your level, and actually lifts you slightly upon contact, allowing you to maintain true infinite aerial combos against large enough Aragami.
Butchery: Can be neat for its concept, but it's only really useful if you're using a blast gun and if you have Power Strike: Bullet attached to it, since CUs trigger before the bullet is fired and only blast gun Aragami bullets have the reliability for high-enough damage every time.
Sharktooth: Another step-based PS that's good for positioning control if you're playing solo and have less than full confidence in your skills. Only rank 1, but it passes through the target, allowing you to dodge attacks depending on your timing and maintain distance. Obvious downside is that, unless you use it from a precise distance away from the Aragami, you'll end up too far away to continue a combo or even dash in for one.
Silverclaw: Great for dodging and taking in lots of Aragami bullets, but its fixed landing point somewhat hampers its usefulness.
Driving Jaw: Another great air PS for solo play. Again, it passes through the enemy, so it's good for positioning control, but being rank 1 hurts it.
Flying Swallow: An aerial version of Sturm. Good if you're not using short blade and either you want better movement abilities or your target runs away in the middle of an aerial combo (but not for much else).
Punisher: A decent air PS that keeps you at a fixed height through the charging animation, but unless you're fighting something big and/or slow, your target will likely move out of the way before you devour.
Type One: As vanilla as it gets. Not bad, but not strictly good either. There's far better options out there. Its only notable plus is its 100% burst gauge for a relatively short charge time.
Type Two: Similarly to Type One, it's not strictly bad, but there are far better options out there.
Möbius: Decent enough for building up Burst gauge and OP, but there are better PS options available for that, and the cooldown after you end the combo leaves much to be desired.
Hell's Claw: It's Silverclaw, minus two Aragami bullets and plus 10% Burst gauge gained. Not worth it.
Downburst: Not the worst option for a general utility devour, but its stationary nature is not conducive to combos, because you could just jump (or use Rising Edge if you're running short blade), freeing up your combo devour (or quick devour) for something more useful. Really, the only reason you should run this is if you aren't using short blade, because it's inferior to Hawk's Flight in just about every way.
Steelfang: It's a rank 3 option for quick/combo/step (well, not step, because that would be a stupid idea), which gives it points there, but unless the Aragami's attention is elsewhere, the long windup animation leaves you critically vulnerable.
Dionaea: Based on the description alone, you'd think that this would be the "best" PS in the game, right? Wrong. Even though it grants invincibility and 100% Burst if pulled off correctly... that's still a ton of time you'd have to put in in order to master the timing, and that's time you could be spending farming for materials, progressing in the story, etc... Sure, you CAN use this PS to pull off perfect no-damage runs against otherwise challenging Aragami, but a) you can do that without this PS, and b) you just don't need it in general.
Type One Fuchsia/Azure/Gilt/Azalea: Loses points even compared to vanilla Type One for how gimmicky and downright insulting they are. There's never a reason to use these, at all.
Golden Relish: All of your stamina for level 3 Burst on your allies? With the huge charge time, it's simply not worth it. If you're looking to run support, go with Orca instead. This is just insulting.
Geist: Literally the LAST thing you want to do in an aerial combo is move AWAY from your target. NEVER USE THIS.