From the new game plus in vanilla P3, you keep your level and your own equipment, alongside your Persona compendium and, if I remember correctly, money. You keep any items you get for maxing your S-Links.

In FES...I don't know how it works in FES. When you upload a file from vanilla P3 (what I did), you get to keep your compendium, and that's about it.

 

Persona 3 was a game that I managed to love and hate, usually one right after the other. I loved the game.. until I hit a boss I just could not beat for hours upon hours of finding the right persona or grinding away levels of Tartarus. Then I'd love it for awhile... until I spent 3 hours going up in Tartarus only to get hit by a Mudo or Hama right before a save point, or have an enemy get to go first and blast the hell out of me with an element I happen to be weak to at the moment - and end up right back where I started, some three hours ago. Sometimes, this would happen several times. I would just keep coming back like a DV case who was certain he'd change this time.

That said - the plot was good, as I've come to expect from most Atlus games, even if Tartarus got boring around level TWO HUNDRED. I liked many of the Social Links: the hard-drinking monk, of course, and the Sun guy, and Tanaka, and Maya, and even the little kid. I'm now playing FES, and using a guide to make sure I hit every max Social Link. It's a shame that you can't have a Social Link with Akihiko, though, or Junpei. I love those guys.