I have only played Persona 3 FES. The premise is too anime / Japanese for my taste too, but I ended up liking the writing / character-depth of the cast. It has a rather dark / bizarre theme that is geared towards adults. May not be great, but it's interesting.
My only complaint is the dungeons you fight in. The game basically has a number of multi-layered dungeons with random generated floors. The deeper you explore, the further you progress in the story (there is a boss fight every 10 - 20 floors you explore). While the exploration / battles are very fun, I've always thought the dungeon designs were something that could have been improved a lot.
Expect to loose to cheap tricks few times during your playthrough. They often throw some OP monsters (or ones that cause status ailments) just before save points, making you loose hours of exploration. Always be on look out for them.