On carbon "flex response": Just as Sailquick, I SERIOUSLY doubt damping properties of carbon vs that of fibreglass has any noticeable effect here. Weight (mass) is what matter the most and then we have to quite common effect of the high end carbon mast simply being stiffer.
I believe that the bow example depends on the same thing, carbon bow being lighter in this case. Its not hard to imagine that there is actually more matter that has to be accelerated in the bow itself than in the arrow. So light weight will matter a lot.
If the actual damping has anything to do with it, I would bet that the type of layup, how fibers and matrix are packed, matter more than the choice of fiber (weight/stiffness effects aside). It may be the case that high end high carbon masts, also sports a "tighter" laminate.