From real life experience; my '87 Ibanez SR-885LE—basswood body, 3 piece bolt on maple neck with Indian rosewood FB—sounds very different than my SGD Scorpio bolt on—cherry body, curly maple top, 7 piece maple/walnut neck, phenolic fingerboard, 2 truss rods and graphite, using the same strings and pickups. The Ibanez has my Jazzbuckers, but I have also tested on them on the Scorpio, but in different cases (narrow aperture neos):
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Then you have these two basses, which are made from the same wood, from the same boards, but have different tops:
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This is an old photo of them, but later, both sporting Hipshot bridges, and my pickups, the zebrawood bass is darker sounding than the maple top bass. Even when unplugged.
Back view:
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So, every part of the bass affects the tone somewhat. It's all a big stew that mixes together to get the end result.
Are the pickups in the same place? Are they the same exact pickups? Same EQ you're using on the tone knob? Not saying wood doesn't have an effect, but there's a lot of confounding variables in your accusation.