For me, I'd agree with two things:
The pickups and electronics, first and foremost.
The player.
The 'tune the tone by the wood' debate will go on and on, but I'd observe three things:
Wood can vary quite a bit, depending on how old, where it came from, how it was milled, did it age/come to the desired moisture content before milling to bass parts for assembly, etc. From log to log, from board to board, from neck to neck, and on and on. And SO very much of this depends on your ears.
I'll admit if you built a neckthru Warwick Thumb in their usual all-African wood recipe, then duplicate it with alder and poplar, both built by the same guy with identical electronics, sure 'nuff, you'd hear difference. But once you start mixing and matching woods (particularly in designer basses with complex wood recipes/laminations), all bets are off. You'd see this with the typical Fender vs. their forays into all-rosewood or walnut axes. On the other hand, though, I've got to admit there certainly is something to it: Fenders are that tone because of alder, ash, and maple, and a Les Paul tone is the maple cap on a mahogany body.
After these years, I think the LESS a body absorbs, the better. In my experience, a workable five-string needs as stiff and hard a neck as is practical to coax out bell-clear low C's and D's, and for clarity up the neck as well. A hard body helps this as well.
My two cents.