It depends on what you're looking for. If you really want to get the whole story, FES is probably the better choice. The games are not specifically linked in plot, but there are holdovers and elements that you will appreciate more if you played the previous game. It's not necessary, but it's a nice bonus.
However, if you just want to play a game, then P4 wins hands down. It takes everything awesome about FES and deals with many of the issues, like blandness of the dungeons (you play these games for the plot and the writing, not the fighting imo), some of the scheduling difficulty, and so forth. It even improves things you might not have immediately thought greatly improvable, like the already-awesome Social Link system, and character development (you really have to see the characters in P4 awaken to their Personas. I'm SO PLEASED with how they did that ).
I highly recommend both games, but if you'll only play one, get P4. If you want to go through them both, I'd suggest starting with FES, but it is possible that you could go either way on that point.
Just a side comment, when these games ask you if you want to play Easy or Normal, suck up your pride and pick easy your first go 'round. Due to the way the battle system works, it's way too easy to get an unlucky fight early in the game and suffer a Game Over or TPK if you don't take a really slow and deliberate path through the game. That being said, the game is set up so that that slow deliberate path is really a viable option. It runs on a calendar basis, so as long as you complete objectives before you run out of time, there's no real penalty for doing so.
I'm just an impatient rube from the Action Badlands, so I steam through the dungeons in a matter of days as opposed to the apparent weeks the game intends. Heh. More time for Social Links!
