I know this isn't what you wanted but here goes. ANY bass in the hands of someone with versatile HANDS and EARS can cover ANY genre, even with just a straight DI on the back end.
That being said, I play a Fender Roscoe Beck Signature. It has two big passive humbuckers that can be split to single, run in series, or run in parallel. There isn't a single tone that I want that I can't get between that bass and my hands and/or a pick. It cops a P pretty well, nails a J, does a solid MM, and even does the neck position mudbucker thing really well.
That being said, I play a Fender Roscoe Beck Signature. It has two big passive humbuckers that can be split to single, run in series, or run in parallel. There isn't a single tone that I want that I can't get between that bass and my hands and/or a pick. It cops a P pretty well, nails a J, does a solid MM, and even does the neck position mudbucker thing really well.