If you didn't have the chance to pick it on the PS2 back then, it's totally worth the purchase for your PSP
For those new to Persona 3 the main story begins with a transfer student (The protagonist) heading to Gekkoukan High School, and moving into a dorm in the city. Along the way you start to wonder what the heck is going on, around Midnight you'll encounter The Dark Hour which only appears after Midnight where everyone around is asleep in coffins. Not only that shadows lurk at every corner and attack anyone who's not asleep in there coffins, you start to find out that you have a special power to summon Persona's.
A group called SEES that live in your dorm asks you to join their group and put an end to the Dark Hour and an unknown tower known as the Tartarus that lurks around school during the Dark Hour after midnight. Throughout the year you get closer and closer to the truth about the Dark Hour and Shadows and of course spending a year in your new school just like what you would do on a normal day.
Gameplay: If you haven't played the Persona series it's really a straight foward RPG game to anyone, the combat while exploring Dungeons in the Tartarus are all Turn-Based/JRPG style game a little similar to what you see in other RPG games like the Final Fantasy series. You can attack normally, use Skill/Magic, change tactics for your party team and change Personas which only you can do. If you weaken the enemies you can do an all-out attack where everyone in your team will pile on and beat the crap out of the enemies.
You'll only be able to have 4 party members in your team and on certain floors you'll find mini-bosses which you'll have to defeat in order to get to the next floor. But however once you've reached a floor and it's blocked you'll have to wait until the Full Moon has passed and defeated the main boss, after that you'll get a phone call saying that the next floor is open. Not only you'll be fighting shadows, you'll also have to rescue random people that randomly step in and go missing.
If you do rescue them you'll be rewarded if you head to the Weapon/Armour shop during the day. If you go Velvet room you'll be able to create and make stronger Persona's if you pick up any cards after beating a random enemy in battle. You'll play a mini-game card shuffle where you can earn a new persona or random item or money.
Not only you'll be battling your through Dungeons, you'll also have to go School for Exams and studies especially if you want to be the coolest kid on top. In order to make and keep your Personas stronger you'll be social linking with friends and other students in after school clubs and outside of school. For your status you can go to certain restaurants, do part time jobs or studies you boost up your Courage, Charm, and Academics if you which can be important if you want to be strong while exploring dungeons or talking to certain people you don't know well. If you have played Persona 3 they've changed the gameplay to On-Screen Cursor you can move the cursor around the field from your school to Port Island.
Graphics and Sound: The only downside to the PSP version is that for those who have played the PS2 version either the original or FES. They've taken out the Anime cutscenes and dialog interaction with other charcters in general are being represented by an on-screen portraits. It can feel like a comic-book up close but the Dungeon exploring is still the same as what you've seen in the PS2 version.
You'll still be able to move your character around the Tartarus Dungeons and battle way through shadows. There seems to be no issues with the camera since they've changed the gameplay to On-Screen cursor for during the day, you can use the shoulder buttons to move the camera around if you wanted to.
You can use the Data Install which can take at least 258 MB if you want to avoid long loading times if you wanted to for your PSP. But I would admit that Persona 3 Portable has some of the most stunning visuals and graphics even if it has taken out a few features and visuals. It's still a great game to view and its art on the charcters have their own emotional faces and feelings. Voicing does a great job if you've played the PS2 version you'll be hearing your favourite charcters again on your PSP.
If you haven't you can expect a really good RPG out of it, but you don't have the option to change it to Japanese voicing if you do hate English voicing in Anime but that shouldn't really bother you at all.
The soundtrack is pretty much the star of the show for the Persona series in general; you could easily listen to the soundtrack all day. If you have played Persona 3 and choose to play the Female Protagonist there are 10 new tracks you'll be hearing if you do play as the Female Protagonist. Music in general is a mix of J-POP and Hip Hop throughout Persona 3 but the soundtrack itself is mixed so there's a verity of themes tunes in P3P.
Overall: If you have played Persona 3 and 4 in general you're going to love playing Persona 3 Portable on the PSP. There's also quite a few other surprises as well including Persona 4 charcters making an appearance including Yukkio if you play the game as the Female Protagonist. Whatever difficulty it on it should take you about 30 hours or more beating the game first round. Once you've beaten the game once you'll be able to carry over your status, weapons and levels.
Hardcore fans will get the most out of the new features in P3P, but if you're new to the series or into RPG games or Anime in general it's worth checking out especially if you're looking for a good game for your PSP. I would say this don't rush the game once or in one sitting because you'll pretty much enjoy playing this game a lot, it took me like 4 months to finish this game but it was so good I did not want the game to end.