Both are outstanding schools. Michigan has a little more prestige, but that isn’t worth much unless you’re trying to get a job on Wall Street. Those people look at the name on the degree.
But the University of Illinois is an outstanding school, and it is particularly strong in STEM departments.
Big Ten prestige doesn’t end with Northwestern, JHU and UMich – Wisconsin, Illinois, Minnesota, Purdue, and others are also very highly regarded both here and abroad, with (each) a slew of highly ranked and regarded programs. Heck, UW was a top-20 university in the seminal years of the USNews ranking, before the publication decided that private schools needed to comprise their top 20 spots, and that the big state schools had to be brought down a peg or two.