I prefer Persona 3. Persona 4 isn't enough of a step forward from it if you ask me.
What I find incredibly weird is that if you compared the story of the two games, 3 would seem like the sequel. 3's story feels like it has much more significance to the world and the Personaverse where as 4's feels far more contained.
Also, the party members feel like they took a step back in 4. Where they are all high schoolers (with varying twists to their tales) in 3 you get a child, a persona weilding robot and a god damn dog! They feel like the type of crazy characters you'd get from a follow up and furthers the feel that 4 is a step back somewhat.
That's not even looking at Persona 3 Portable, which takes all the combat redesigns from 4 and adds them back into 3 and lets you play as a girl, which is just as fully fleshed out as you'd expect.
Persona 3 wins, quite handily, in my eyes.