P4 is overall a better Game/Story however P3 has its own unique style and you frickin shoot yourself in the head.

Overall P3 and P4 have animes lined up for them.

I still need to play P4 (Dusts off ps2)

Nice timing, I just finished P3 a couple weeks ago and have been going apeshit in P4.

Persona 3 was an ongoing experience for me, I had borrowed FES from a friend and got a little over half way through the game before my memory card decided to format itself, I tried starting all over again but I couldn't muster the will to go through Tartarus again. I wound up giving it back and eventually forgot about it completely.
I only remembered it when I saw the PSP version down at my local Pawn shop for a cool $10. After buying it and cleaning it up, I played it for about a week before someone stole my memory card. So again, I had to start over but hadn't the will to do it. A couple months ago, I started going through my backlog and it happened to show up. Beating that game was just about the greatest feeling I've had all year and I'm really glad I picked it up again. Next I found P4 and decided to give it a whirl, I started playing that less than a week ago.

Character-wise, I like P4's better so far.
The MC feels much more human and the party members are less half-assed than the ones from P3 (I'm lookin' at you Fuuka...)

I'm not very far into P4, so I can't really say anything about the whole Serial Murder shtick P4's got going on.
P3, on the other hand, is pretty damn awesome. The whole game is centered around despair yet somehow stays cheery and bright most of the time. It reminded me of suicide, honestly. The Evokers, the dark atmosphere and the end made everyone think all hope was lost and it was pointless to go on. I haven't played a game in a long time that compares to the story told in P3.

As far as gameplay mechanics go, I think they're both pretty much the same, give or take a few functions.

One thing that P4 has better is the group dynamic. P4's events show that these are your homies. They gather, they talk, and share experiences. P3 was lacking. Most of the time I felt that they try their best to avoid each other during the daytime and only get together when going up the tower. Though they did get to hang together more often near the end but I felt it was kind of forced (most likely forced by the situation).

I liked P2 far better. you were just so on rails with all that High school bs in P3.

I've played P3:FES and loved it, so I bought P3P. I thought the characters, social links, and evokers were great.
I still need to play P4. *sigh* (backlog)

P4 is my favorite game by far (trumping Chrono Trigger which had ruled for the past 15 or whatever years). P3 was close and I loved it enough to get FES and play it again, but I didn't love it enough to play "The Answer" right away though (but I would like to eventually).

I generally like the characters in P4 more (but Junpei > Yosuke), like what others have already said (you actually get to socialize with them, etc).

Also part of the charm of being in the boonies is the country atmosphere and characters.

Love both P3 and P4. Finished FES and still working on P4.
I did like the style of P3, but I loved the setting of P4 in that it is in a more rural part of Japan. I lived in a rural part of Japan and it really appealed to me personally.
It should be mentioned that the the music in both games is fantastic!

I can totally see the reason why some people prefer P4, but I've been a city slicker my whole life so the rural thing holds no personal appeal. I agree that Fuuka was a character epic fail, but other than that I'm more fond of P3's characters than P4's.