It really is hard to get on with a Jazz when the sound in your head is the Precision. BUT, a Road Worn Jazz is a great bass stock, so I would never change the pickups as they do the signature Jazz thing more than adequately.
Having both pickups on full is quite an alien sound when coming from a P but the beauty of a J is when you start backing off the volume on one the other or both pickups. This is where the genius of it's design comes to light.
I also believe that the thinness of sound that is a common complaint is much better addressed at the amp than changing out the pickups.
Just think of Led Zeppelin or Bob Marley and the Wailers. All recorded with Jazz basses and no one can complain that JPJ or Family Man had a thin tone.
I'm a total P guy btw, but a J eq'd correctly is wonderful.