I was a bit wary when I heard that Atlus had to scale back some of the content to fit this onto the PSP, but eventually my curiousity got the better of me and I gave it a shot.
I wasn't disappointed, for the most part. Everything that made it good (to me) is still there; the game play, the battle system, lots of Personas to collect, Social Links, etc.
The only thing I would really rate down is the fact that the cutscenes are essentially gone, and replaced with visual novel style story telling, where you basically read the text and imagine what is going on. This wouldn't be a bad thing, I personally enjoy VNs, but then, VNs typically have a lot more narration to explain what you can't see, so you have something for your imagination to go on.
Unfortunately, while the dialogue is all intact, with full voice, there isn't much to explain what is happening beyond some sound effects and the characters gasping and exclaiming as appropriate. If you've played either of the two original versions of Persona 3, its not a big deal, but for new players it might be confusing.
But those are just minor complaints, and even if you haven't played Persona before, I think you will enjoy this game. And for those who have, the things that made Persona 3 great the first time are there, plus plenty of new things to check out. The new female MC is cute and a lot of fun to play with.