There have been studies showing how flat back and carved back plates vibrate. There is a big difference! However, interestingly though neither experts nor non experts could successfully tell the difference between the two in blind listening tests.
iirc the difference is that properly graduated, carved violin style bass back plates have even resonances that are equally space apart while flat backs with cross braces have distinct peaky resonances from the braces stiffening effect.
Keep in mind though that these listening tests were the same model basses with either a well made carved back or a well made flat back bass.
My take on this is that a carved back has the smoothest, most even response but the flat back can be constructed in a way that has evenly spaced resonances by bracing it to flex in a similar way.
Smoother or more even resonances are not superior to a more "reedy" or peaky, viol sounding bass, only different.
I try for evenly spaced resonant back. I use thin, light braces that are X shaped and curved to a radius, resulting in the back being dome shaped which create about a half inch of curve from end to end and side to side. Even the area above and below the break angle is curved in the dome shape. The reason is to mitigate against cracks and to create a flat back that behaves like a carved one.
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