The ultimate capacity of a member in bending is definately related to the Tensile Stress (Fu). This is not the same as a design level requirement you are talking about.
However, the shape factor is really a measure of how much reserve capacity you have in a cross section until EVERY FIBER HAS YIELDED where as the Sx modulus is when the initial extreme fibers yield. It's the difference between intial yield and total yield.
While I was writing this, Scott Maxwell posted and adequately explained what I was going to say.