P3P is a worthy port as well as extended story of the two prior games Persona 3 and Persona 3 FES.
Not only does the original Male story fit back in, an adapted Female version enhances the game even further.
Graphics: 7/10 Most of the game outside of Tartarus is on a flat digital background, with the main character as a blue or pink cursor. This hurts the game just a tiny bit because exploring is not over the shoulder. Walking through the beautiful Gekkokan High, or Port Island station, or even the Mall was fun because you could go explore to a certain degree. The P3P method is instead a hovered omniscient view where you hover the cursor over a selection of places you want to go. But fear not! Because the goodness of 3rd person travel is restored upon exploring Tartarus, where the PSP adaption shows it PS2 origins. Another hit the game takes is lack of anime cutscenes. If you loved the cutscenes from the game, they're replaced with snapshots of certain points of the cutscenes, and just sit on the screen as character talk, eventually cutting to a different picture. IF you didn't like the cutscenes, then lucky you.
Sound: 10/10 Same beautiful soundtrack as Persona 3.
Gameplay: 9/10 The battle system has not lost any bit of potency and is still fun just as fun as the original. What makes it even more fun is that these battles the player doesn't feel obligated to go to a certain area. They have free range to explore as much of Tartarus as they can, and spend as much time as they want (until their character tires out). Even outside of Tartarus is fun. Despite not being able to explore as much, traveling is MUCH faster, making it seem like there's a little more time to enhance the main characters social status and attributes.
Story: 10/10 You all know the Male's story, and the Female's story is no less brilliant. Given it's the same, yet altered in slight ways (such as the bath house scene). Also many new social paths are opened up to the Female which is cool, because it feels like finding hidden treasures upon encounter.
This game had many more innovations than shortcomings. If you own a PSP this is a definite must have, even if you've never played any Persona games.