Assuming that there is no limit on student body size, how would a school that was originally thought to be better compare with the other school(s) in equilibrium?

Consider a school choice program in which each student (or the parents of each student) can choose the school that he or she will attend. Assuming that there is no limit on student body size, how would a school that was originally thought to be better compare with the other school(s) in equilibrium?