I want to know your definition of "essentially no difference"... Frankly, Stanford and the U don't belong in the same sentence in terms of level of academics in my opinion, and that is no shot at the University of Minnesota at all.
http://colleges.usnews.rankingsandreviews.com/best-colleges/spec-doct-chem
That is what I mean by no difference. In most engineering fields, take the top 5 or 6 and really there is no difference. Most years we are between 1-4 in chemical engineering at the U, and that's statistically where our smartest kids go.
If you want to compare sociology departments go ahead, but I'm more interested in comparing our best departments to theirs. Overall, yes, Stanford's dumb kids are smarter than the U of M's dumb kids. Most football players fall into this category. If you are smart enough, you can go anywhere, and a lot of these kids know that Big Ten schools are every bit as good as (and sometimes better than) Stanford, Caltech, or MIT, depending on what you want to do.