Surely there must be someone who has tried to resolve this question beforehand in a systematic way? Maybe a luthier as suggested by CrazyKiwi?
If you look at the main visible source of sound - a string visibly vibrating in a magnetic field of the pickup effectively secured at both ends against the metal of the fret and the bridge versus the miniscule flex/resonance of the wood then I find it hard to see how the wood can make much difference to the sound in comparison. Surely minor variations in pickup configuration, maybe even the electrics variation from bass to bass may make a difference, and that could be attributed to the more visible 'wood' attribute in otherwise identical instruments.
That said I am perfectly willing to be convinced otherwise! I find it quite surprising the emotional investment people put into these discussions. One way way or another basses do vary significantly and we all enjoy exploring the differences...