@Alexandre and @rjkofnovi, UMich may spend a ton of research money, but that doesn’t mean that it would rank at the very top by whatever research criteria that a research ranking uses. UW-Madison is similar in having huge research expenditures and ranking right around UMich in ARWU.
I’ve noticed that UIUC is another Midwestern B10 flagship who’s CS department fits a similar pattern: UIUC CS is considered among the best, but the top 4 in CS in terms of prestige are MIT, Stanford, CMU, and Cal. However, UIUC CS blows all other CS departments away when it comes to getting research money. It also (like UMich CS) has a reputation for being practical (as opposed to theoretical, which is where UChicago CS and the top UK CS programs are at). It could be that with the cutbacks in state support, good flagship STEM programs are incented to focus research on areas where there is a lot of funding available rather than sexy prestige areas that don’t bring in much money but are more likely to win awards and publication in prestigious journals.