Mica,
I can usually identify certain bass players the moment I hear them. Of course, Jaco comes to mind, as does Stanley Clarke, Chris Squire, Geddy Lee, and John Entwistle. I can also usually identify certain types of bass guitars (Precision, Jazz, Rick, Thunderbird) or bass guitars like those marks.
As for obscure stuff, I can almost always identify something that is Frank Zappa, early Genesis stuff, King Crimson, etc.
I will say one thing, though - one could hand two people the same instrument, and it would sound completely different. For example, if someone gave me Entwistle's instruments, or Clarke's, or Jaco's, it wouldn't sound like them. It would sound like me playing their instrument, for better or worse. So much more goes into tone than just the equipment itself - touch, hand placement, muting, picking, fingers, etc. That has as much to do with tone and voice as does the choice of instrument itself IMHO.
Alan