Yes. There are some obvious differences, but overall I would say these two are pretty similar in the grand scheme of things- large state schools in the midwest with a substantial East Coast/OOS/Jewish/international presence, great college town, wide range of students and interests. Michigan is more football oriented compared to IU whose forte is basketball, and obviously Michigan is much more selective. In Michigan, the University of Michigan is excellent in pretty much every department, and Michigan State is a clear notch below in terms of selectivity and rankings...whereas with the two big Indiana state schools (IU and Purdue) they are kind of split between what they "specialize" in and top students in the state seem to attend both in fairly equal numbers depending on their interests. IU is more liberal arts, business, and music; Purdue is all about engineering, Stem, and ag. IU is more Greek than UM.
I would also add University of Wisconsin to complete the "trifecta" of big midwestern state schools that attract a lot of East Coasters, good school spirit, awesome college town.