It's a genuinely tough decision but I always weigh in on Persona 3 as the better game. I prefer it, though the two are both so fantastic that you couldn't go wrong either way. The story in P4 was a bit more convoluted, but the characters were charming and the way you needed to acquire each new party member (I'll keep that vague for those who haven't played) is awesome.

Still, at the end of the discussion, P3 gets my vote if only because Tartarus was so damn good. I loved how closely it felt to Nocturne while integrating all of the Persona 1 & 2 quirks. Plus, MITSURU