I LOVED Persona 4, but never finished because my PS2 broke. I tried, but couldn't get interested in the narrative here. I am a big fan of the fighting games made by this developer, though, so I had high hopes.
The Street Fighter style fights are kept very simple in terms of the number and variety of moves each character has. Where it gains it's depth is through the universal-to-all-characters counters, cancels, and advanced techniques. If that doesn't make you drool, you probably won't spend much time fighting.