Like HurrayForums says, it depends on if you like the JRPG elements with a dash of the social sim stuff that is also a genre in and of itself in Japan. If you haven't been indoctrinated into that, it might prove to be a jarring experience.
But as someone who plays and likes console RPGs in general, it's a solid game. It'll give you plenty of game time, the social elements provide an interesting diversion from the normal hack and slash, and the battle system is balanced with a few unique elements (knockdown via rock-paper-scissors type system, persona combinations, and the like). I prioritize story above a lot of other elements in RPGs as well and the story is engaging and fun, if not a little bit campy - but if you've ever watched any anime series to its conclusion that's a good thing, not a bad thing.
Replayability is low, honestly, but you get so many hours out of it that it's plenty fulfilling. I'd get Persona 3: FES if you're interested in more of that, as that has even more hours of gameplay. Persona 4, though, seems to improve on some of the not-so-good things about 3.