Since this has devolved into yet another endless tonewood debate, I'll throw my piddling unscientific experience into the ring for general condemnation, if you've read my little Tonewood diatribe before, please ignore:
I have a 1986 Steinberger XP-2, CF neck, epoxy painted rock maple "flying vee" shaped body, looks just like this one:
Nothing wrong with it, a superb sounding and functioning bass in every respect, I just got tired of the dated 80's look, and very trebly sound, wanted to "warm up" the tone, maybe get a little more bass fundamental out of it if possible.
I transferred EVERYTHING, neck, electronics, bridge, neck bolts, and even strings (they were new, and in a very light guage that's hard to find) from the original body to this ho-made mahogany body. Not a masterpiece by any means, but it's more comfortable for seated play, and gives me a place to rest my forearm, and it was a fun first body build. The only parts not relocated were the pickguard, misc. screws, and the flip-out knee rest. The only change therefore, was the body wood, from rock maple to one-piece mahogany. The maple body has some kind of bulletproof, thick finish on it, the mahogany was finished in Watco Danish Oil. The weight feels roughly the same, though I haven't weighed it, but that should be irrelevant if the wood has no impact on tone. I accept that a change in MASS might have some effect, maybe on sustain, which does seem slightly less with the new body. I spent a great deal of time getting a finger-tight neck pocket that bevels inward along it's vertical and lengthwise dimensions to match the original neck pocket. The beveled neck cross section allowed Steinberger necks to be cleanly popped out of the mold, a HUGE PITA to re-create in a wood body, let me tell you, so I'm pretty confident the neck pocket was nearly identical to the original.
I had hoped to get a warmer tone out of it, and it's definitely more resonant unamplified, but it's also warmer and bassier plugged in. This having been my goal, one could say I'm just a victim of wish fulfillment, but a couple other bass players, who knew what the Steinberger sounded like, also remarked on the change in tone, so I think there is something there. I have no before and after soundclips to offer as proof, so I don't expect anyone to believe me, or share my conclusions, but it HAS convinced ME that the wood has some effect. This is only interesting in that I inadvertently created as close to an isolation of body wood as a tone generator as I've seen on TB. If somebody has a convincing explanation for why changing the body wood has changed the tone, I'd be genuinely interested to hear it, I still have an open mind on this subject.