So lets go for the more powerful one!
Interesting in Browns results is that the observation that the player is often able to mask or compensate for the difference in response between roundback and flatback so the differences are un-noticeable. I suppose if the back is contributing significantly to tone and volume you have a built in tone filter available with your left knee.
My observations of a free plate oscillating at a low resonant frequency, where the edges and centres of the plate can move by a centimeter or more, lead me to believe that a flexible rib structure helps allow the top to move, which is essential to transform string energy into movement of air, thus sound. The controlling factor is the strength of the box which must stay intact under high tension and compression. So you can see how both the schools of thought can work. But for me I think the back has a structural priority while its resonance is a by product of what's going on elsewhere.
Understanding its role in tone production I agree is not science yet!
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