When you draw a bow across the strings, you are imparting energy into the combined physical system of the violin and the bow. What you want is for as much of that energy as possible to be transmitted to the strings, which transmit it to the bridge, which transmit it into the violin and then out to the air.
Like anything else, a bow isn't 100% efficient; inevitably, it will absorb some of the energy and reflect some of the energy. The stiffer the bow, the less energy it absorbs and the more it reflects back into the string. So a stiffer bow is preferable because more of your energy goes into producing sound.
This is the same principle as with graphite tennis rackets and baseball bats. The stiffer the material, the more the energy is transmitted where you want it.