Persona 4 takes what was good in 3 and makes it even better.
Is it really that much of an improvement? Judging by some screenshots and the soundtrack the overall tone has clearly changed since 3 but did they update much else?
-Allies can take hits for you, endure one fatal blow themselves, use Follow-up Attacks and cure status ailments for you.
-No more Tartarus. Now you get to kick ass in the TV world, with like a handful of dungeons with unique catches to them. (lolvideogamedungeonlol)
-Has more of a 'mystery novel' edge to it. (aka: you have to figure out who the killer is, and what his intentions are)
-Some new Personas. I'll leave you to figure them out, assuming you do get the game.
-Kuma is gay. >_> <_< *cough*
-Overall game is easier than P3.
-Physical skills are actually useful now.
That's all I can think of, off the top of my head.
EDIT: Forgot to mention, you can now directly control your teammates, so there's less chance that they'll screw up a battle that you normally wouldn't have trouble with, unless you''re as stupid as your teammates in P3.