The amount of power a mechanism delivers depends on how fast it transforms potential energy into kinetic energy. If the energy stored in a twisted rubber band is released over a short time it delivers more power than if that same potential energy is released over a longer time.
Wind-ups with small wheels convert potential energy into kinetic energy more rapidly than wind-ups with big wheels. Thus more power is delivered to the small wheel making it turn much faster than the big wheel, although for a shorter time.