Disregarding technique, which really is IMO a massive factor, SETUP is massive. String type, action, relief, fingerboard profile and saddle break angles all contribute to the overall tone. The same bass with a slightly higher action and a little more neck relief will sound different to a low/straight setup.
The pickups and electronics can only capture what is there to begin with and cannot put back what is not there, so they are next in line. I guess some pickups are so bad that they cannot even capture what is there (and that is a whole different hill of pain) but correct positioning and balancing is essential to get the best out of any pickup set.
After this I think everything else is a matter of taste. YMMV, of course.