I messaged the Atlus QA guy Rob Stone about if a (this is the first time I've ever wanted a remaster by the way, or re-release) Persona 3 re-release would happen consolidating the pros of both games into one game since it's always a hard decision to pick which to play and he said there was no official word of another P3 release. Then he recommended me the PSP version because "the content that isnt there isnt really significant when compared to how much better the game mechanics are in the remake." They also said they'll take what I said into consideration but I doubt they'd release another heh. I guess P3P it is. In addition to this guy, the majority of recommendations have been for P3P.
I started with P3P, then switched to FES about 10 hours in. The difference was enough for me to abandon P3P immediately and start from scratch on FES. I got into Persona because of it's story, not because of combat. Funnily enough, despite what people say about Persona 4 Arena, watching a friend play P4A (Labrys' story, to be exact) is what made me drop everything i was currently playing and buy P3 and P4 the next day. Even though FES has gameplay flaws, only reason i went with that is because how much i didn't care for combat, and wanted the best story i could get. I've only recently started warming up to turn-based combat, but my entire driving point in P3 was story, and nothing else.
That's my personal opinion on why FES is better, but some may argue mechanics are better than story. Normally, i'd agree, but P3 is the first game to ever pull me in as hard as it did. I beat it in 60 hours, and in 6 days. 10 hours a day. I have never been hooked to a game that hard before solely from story.
Don't take this as me telling you to play FES. This is my opinion, and my opinion alone. P3P does have a better combat system, and full-party control, along with other Quality of Life additions, and FeMC.