1: The stats comparison.
Special Attack: 103
Special Defense: 71
Special attack: 54
Special Defense: 86
- Greninja and Barbaracle's HP are equal, 72 = 72.
- Greninja's Attack is slightly better than Barbaracle's, 95 > 92.
- Greninja's Defense is weaker than Barbaracle's, 67 < 115.
- Greninja's Special Attack is better than Barbaracle's and by far, 103 > 54.
- Greninja's Special Defense is a bit weaker than Barbaracle's, 71 < 86.
- Greninja's Speed is so much better than Barbaracle's, 122 > 68.
2: The relevant details
Greninja assumes a plethora of roles, as being a scout, an annoyer or even a sweeper. It has a pretty good typing, resisting 7 types, and being weak to 5 is a good deal. But what makes this even better is Protean. The Dream World ability of this ninja provides him surprising battles. For example, against Conkeldurr, it can use Extrasensory and change to a psychic Pokémon for an OHKO, or if not OHKO, it would resist Drain Punch, but I believe Conkeldurr will use Mach Punch to pull it off the way. Greninja is weak to Mach Punch; this prevents it from abusing its ability and destroy it as well. It has access to a pretty diverse movepool. It's definitively a strong one.
Barbaracle lacks a true role. It has a normal typing, being weak to 4 types and resisting 5 ones. Not bad, but Greninja resists more. Barbaracle has 2 abilities, Sniper won't be used because Though Claws outclasses it. You have Razor Shell, Stone Edge, Earthquake, Cross Chop, X-Scissors, Night Slash and other options. It has an OK movepool, but you won't use its average stats. Any upcoming Energy Ball, from Galvantula for example, will KO it. There is not much about Barbaracle.
3: The Choice
Greninja. Simple as that. By far it's better. Now, for in-game use, Barbaracle is worthy of a try, and every Pokémon can be beast in-game but competitively, unless it's for lower tiers, Greninja is simply the best choice.
Hope it helps ;)