Honestly, get both. Persona 3 FES has a 3D world map that you can walk around in, while P3P is basically backgrounds with icons, kind of like a point and click adventure. There are also no anime cutscenes in P3P. The epilogue titled "The Answer" that takes place sometime after the main story is only available on P3 FES as well.

The bad thing about P3 FES is that you don't have complete control of your party members. Instead, you give them tactics and they'll act accordingly. The only member who you can fully control is the main character. In P3P, you have full control of everyone. Also, P3P has more Social Links. It also lets you play as a female character, changing a lot of the Social Links and replacing some.

In my opinion, I find it best to first play through Persona 3 Portable, then play Persona 3 FES solely for the epilogue "The Answer." In P3 FES, you can play the epilogue without having to play the main story.

Should have just made Portable 3rd G, or even Portable 4th for Vita. Freedom Unite / Portable 2 G was really fun. I have a 3DS for Monster Hunter 3 Ultimate if I ever want to get it. For now I'll stick with Soul Sacrifice.