I agree with pretty much everything Airk said regarding the gameplay improvements/refinements to P4. Specifically…
The ability to individually control your party members eliminates the frustrating Mitsuru effect.
The dungeon environments are much more varied compared to Tartarus.
Managing your party’s equipment is much easier (I felt this was pretty unwieldy in P3). You don’t have to go talk to them to change their equipment, you can automatically equip/sell old gear when buying new stuff, and so on.
You can use the square button to quickly move to different world-map areas, instead of having to run to the exist (seems small, but it’s pretty convenient)
When viewing a persona or selecting skills in battle, you can view the effects of the skills (eliminating the need to memorize names like Agi, Bufu, and so on. But after playing P3 you won’t need this for the most part).
When your party members level up and gain new skills, you can choose which old ones get replaced.
I’m only about 40 hours or so into P4, so I can’t fully comment on the story, but so far I’m liking it just as much as I did P3. It has a different tone, to be sure, but I still think it’s great.
About the only thing that I don’t like more in P4 is the music (but the song that plays while you’re walking around in the school is damn good).