I've always like Jazz basses better. I have a P now and have had a P in the past. They are cool and fun to play (with a J neck on them). But, they just don't have the same sound and I prefer the Jazz sound along with the feel. I like my P and I will take it on a gig every now and then for a change of pace. It sounds good and is fun to play, but what it really does is when I put it down and get the Jazz back out, I realize how awesome it is.
Now, the Jazz basses can be different too. I have a USA Geddy and a USA 75RI and they differ a bit in sound. The 75 is just a tad bit more tame. While the 75 is definitely the best looking of my basses, it probably gets played the least. Not a knock on it as it is a wonderful bass, just something about the Geddy that is just right for me. And the P is still new so I like playing on it.
One think I really have to remember is to make sure when I get a new pedal, to test it out with the Geddy. That is the bass I play live most and I have recently had a couple of pedals that I didn't like that much and was testing with the P. Once I went back to them with the Geddy, it was a different ballgame.