That is THE question!!
Look at the Precision and the Jazz, you'll see the pickups are different in both, naturally meaning the sound from each will be different.
The J v P debate will rumble on until the end of time, the best advice I can give you is go on YouTube and listen to comparisons and see how you feel.
Maybe check out your favourite bass players and see what they play.
For me, when I think of a pleasing bass sound, it comes from a Precision. It is "the" bass guitar sound to my ears. I'm sure I read a quote saying it's the most recorded bass guitar in modern music history and there's a very good reason for that.