Well, It really depends on what role you want. Greninja works best as a fast special sweeper with coverage, and azumaril is more slow and bulky, with coverage and equal attack/special attack.
Here is a good Greninja set:
252 sp.atk/252 spe/4 HP
• Dark pulse
• Ice beam
Greninja works well because he has the two essentials for a sweeper: high special attack/attack and speed. Also, he has the awesome ability protean, which gives him STAB for every move, plus it throws the opponent off the trail when it comes to landing a super effective attack. However, its defences aren't too great, which means it can't always survive if the opponent is faster, or is bulky enough to survive one of its attacks. You just need to know when to switch when using a Pokemon like this. This can be helped with u-turn.
Here is how you might use Azumarill:
252 atk/252 HP/4 spe
• Aqua jet
• Play rough
• Aqua ring/maybe another attack
This can be used for lots of coverage too, and despite its low speed, it can still attack first with aqua jet. Its high HP and aqua ring set up plus leftovers can hold out against the opponent for a surprisingly long time. And its access to the ability huge power is also going to help with all its attacks. However, if faced with a Pokemon of similar stats, and a resistant type, its attacks won't do much, and the opponent will be able to break past its defences.
Or there is always this set:
252 atk/252 HP/4 def
• Belly drum
• Aqua jet
If it uses belly drum, then aqua jet it is practically unstoppable. Unless the opponent has sap sipper, or has high defence/HP and is of resistant typing, then this set will fail.
So, both Pokemon have their up-sides and down-sides, but overall, Greninja is generally more useful, whereas Azumarill, having lower attacks, won't be as useful in the same role. So that means it really comes down to the question of which role is more useful. And again, I think Greninjas is.