On 70th ish floor and haven't played it in months......Devil Survivor came out and I haven't been about to put it down. It has a better battle system IMO as you actually get to fight with your summons and the story is one of the best ever.
So I vote to add Devil Survivor in the P3 and P4 fan club.
I think I like the flow of the story, characters and interaction of Persona 4 slightly better, but I thought the bery last ending of Persona 3 was executed better. The concept of "persona" is subtly different between the two. HOWEVER, To get the "true" ending of Persona 4, was hilarious in the JRPG context.
Persona 3 FES was the first JPRG I maxed out all my characters.
And no, you don't have to play 3 to play 4. They are seperate games, although there is at least one reference to 3.