jazz basses are generally deeper and smoother, while precision basses are more for stingy, accented sounds. depends what kind of sound you want or what style of music you are into, like slapping is usually associated with jazz basses. personally, i own a fender standard jazz bass and prefer it to any precision bass. do some research and you should be able to figure out what you like best.
Jazz - 2 single coils thinner necks deeper sound
P - 1 split coil thick neck punchy sound.
'J's sound smoother, 'P's are punchier. Personally, I prefer precision basses in every way. I'm buying myself a MIM 'P' in December.