If you loved Persona 4 for its characters, then you might want to give this a try.
If you loved it for its gameplay, then don't bother.
If you have no clue what the Persona games are but you're a fan of fighting games, this might be okay if you don't mind not understanding what's happening.
If you loved Persona 3 and just want to see Mitsuru in leather and Akihiko shirtless, then by all means play this game. (Or look up the artwork online.)
The nameless, voiceless main character of Persona 4 has been assigned both, and Yu Narukami is back for a visit to Inaba a couple of months after he and his friends solved the mystery of the TV murders. When he arrives, however, it quickly becomes clear that the TV world is also back, and Yu and his friends are being pitted against each other—apparently by their other friend, Teddy. In addition to the P4 gang (yes, Kanji still fights with a folding chair), there are guest appearances by a handful of P3 characters as well, so if you've missed Aigis, she's here for you.
I played this on the 360, and the elaborate controls for all of the moves frequently don't work. It's possible that the PS3 version mapped better, but I have my doubts.
Arena is a mediocre fighter and a poor sequel. What it is, also, is the product of a great company taking a chance by not staying in their safe zone. Even though I didn't like the result I have nothing but respect for the intention. I hope ATLUS keeps producing new, unique games without fear of alienating their customers. I, for one, am happy to have the odd flop if it means I can still have intelligent, creative, and not-at-all safe games.
Of course, it doesn't hurt that they're always incredibly pretty, too.