Physical is lame. There is a decently noticeable power drop-off (lower Attack stat, physical STABs have less BP, and Aerial Ace is a very weak coverage move) so Greninja is much easier to deal with.All the above combinations are great and all, but that's assuming that people receive that nature when they transfer their Ash-Greninja to either Sun or Moon from the demo (mine had a Lonely nature when I transferred it)
This combination would be for those +Atk natures (or Jolly)
Greninja@Choice Band/ Water or Dark Z-Crystal
Ability : Battle Bond
Nature : any +Atk nature or Jolly
EV's : 252 Atk, 252 Speed, 4 Special Defence
-Waterfall
-Night Slash
-Aerial Ace
-U-Turn
Because of Greninja's initial base 95 Attack, the best chance for it to activate Battle Bond would be to faint one of the opponent's pokemon with a super effective attack or U-Turn against an opponent's death fodder. After Battle Bond activates, base 145 Attack with base 132 Speed is nothing to sneeze at.
Waterfall and Night Slash I believe are Greninja's best physical STAB's, each also has an additional effect with Waterfall's flinch chance and Night Slash's higher critical hit ratio, which could possibly help if hax is on your side. Since this is a Choice Band set, U-Turn would be used for getting extra damage and pivoting into another team member to take an attack that Greninja wouldn't be able to. Aerial Ace might only have 60 base power, but covers some of Greninja's weaknesses (Grass, Bug, Fighting), you could run Acrobatics instead if you decide to have Greninja hold a Z-Crystal, since after the Z-Crystal is used, Acrobatics has a base power of 110.
Any +Atk nature (especially Brave) would be outclassed by Jolly since Greninja relies on it's speed to K.O opponents. However, if you knew exactly what you could outspeed with a +Atk nature, then you'd still be able to stay alive and be a problem for your opponent.
Also, Z-Crystals are not consumed after use, so no boosted Acrobatcis.
To my knowledge they are being tier separately. If BB does end up in Ubers, it will not be able to function because getting that first kill will be exceptionally difficult with all the fatmons (plus Primal Groudon laughs at Greninja). Deo-A exists if you want a fast, frail nuke, and it doesn't need to nab a kill to be a threat and got a new best friend in Tapu Lele.Honestly, one of the biggest problems with Ash-Greninja in singles might just be which tier it lands in eventually. I'm pretty sure it's different enough to warrant a (potential) separate tier placement, similar to therian formes for Landorus, Thundurus, and Tornadus, but it really comes down to whether it's consigned to Ubers or gets to enjoy OU. If Ubers, it's gotta hit hard, so almost without a doubt it'll need to run a Choice Scarf or Choice Specs. If it ends up in OU, it won't need to hit quite as hard and the versatility it might get out of a LO and/or a possible mixed set (highly questionable) could be more important.
As for Z-crystals as the held item: I'm a little iffy about Z-moves since they only get one use and then leave you itemless, but Ash-Greninja might benefit from it, if for no better reason than that it will get the KO to activate Battle Bond in a tight spot.
No analysis of classic Greninja from me, it's just too obvious.