I've recorded a fair share of good basses and I can say that:
1) Jazz basses ALWAYS work for everything. You can find better things for a particular style, but they work OK for everything. The Marcus Miller sig J-Bass is AWESOME, btw.
2) Precisions don't work too well for modern stuff, due to a higher voiced sub bass.
3) That Sting signature P-Bass only works for light stuff.
4) Had a couple of Warwick basses on the studio I work on, and they're OK, but their tone is kinda mellow, lacks a little bit of clanckyness for rock.
5) The only Musicman Stingray I've ever recorded sounded like crap, maybe it was a bad one.