It's interesting...the only bass I've ever owned out of the box that sounded distinctly different to any of the others was a Rickenbacker 4003 and even after about fifteen minutes of dialling in my tone it sounded virtually the same as the rest of them. That's the thing; I know what my tone should sound like and I've kind of known that for 25 years or more, so my expectation of that gritty Geddy Lee/Jean Jacques Burnel sound will always be there. I have a £25 Aria Primary and a £3.2K Lull (and a few in between), they all sound fairly similar once I've had a noodle 'n tweak.
Heh. I kind of know what you mean - I sound like myself no matter what I play -- but on the other hand, of the four basses I currently have, the two that are closest together are the Gibson LPB-1 and the Greco Thunderbird, and to me even those are pretty different - the Greco has a lot more in the medium-low mids, the LPB has more articulate lows. The other two (Ibanez Blazer with Alembic P/J activators, Danelectro DC reissue) sound nothing like each other and nothing like the Gibson-ish instruments. Sure, I sound like myself on any of them, and given enough EQ I can get something to work ... but
I still care
I also had and sold an EB-0 and it sounded nothing whatsoever like any of the others :-p