While I think P3 is the better game, I like P4 more. The stories are equally good, even if 4's a bit more convoluted. The themes are also both pretty profound and well thought/out, but the characters of Persona 4 just take the cake and make the whole ride a blast.

Also, gameplay-wise, P3 is better, but 4 does three individual aspects better. One - character Ai is now optional. Two: female social links do not default to romance. Three: the TV world is soooooooo much better than Tartarus. A bunch of smaller dungeons is way less tedious than one 300-floor monstrosity that's the same throughout the whole game.