Thanks for the responses! For what it's worth, here is what the department head at a top program had to say to me on the matter. I also have an offer from Cornell.
"They are all great PhD programs, but I'd rank them CMU > UM >> Cornell. I'd probably rank CMU's Statistics department equal to Harvard's, if not better. It has more breadth and depth, and many terrific faculty (including two of my former PhD students, and ). CMU has long been a leader in statistical computing, too.
We would hire from any of them: we look at individuals' work, letters of reference, research and teaching statements, publications, etc. But we do consider who wrote the letters of reference...
Congratulations on having several great choices!"