What are the "intangibles" that distinguish one university's CS program from another?
Fair warning, I am not intimately familiar with the programs, and my answers are based in some stereotypes of the institutions and the CS programs.  However, given that my answer is based on student selection, institutional reputation may not be a bad way to think about it.

While Yale is, by any measure, a top-tier institution, CMU is (at least by reputation) possibly the top computer science program in the world, and at an institution that is otherwise ranked lower than Yale.  I would expect, then, that self-selection among students would play a huge part in this. The sort of student who would aim for CMU for CS would be doing it because the opportunities for CS at CMU particularly appeal to them.  

By contrast, the sort of student who would aim for a CS degree at Yale would be the sort of student who is aiming at Yale first, and also wants to major in CS.