As you see from my signature, I'm a dyed-in-the-wool Precision player. The Jazz bass I have simply because I'm a sucker for CAR with a matching headstock. It is rarely played and the body shape is really awkward to my eyes.
Generally, I find a Jazz neck a bit narrow. That said, the B profile on all my Precisions is only a little wider, but significantly so for me. Similarly, sonically, the Precision does everything I want a bass to do.