@bkamber for what it’s worth here are the US News rankings on undergrad. engineering:
UW-Madison: #14 overall; #25 biomedical; #5 chemical; #13 civil; #14 computer; #19 electrical; #9 industrial; #17 materials; #17 Mechanical.
UMTC: #22 overall; #18 aerospace; #3 chemical; #19 mechanical. Other categories not ranked/not in top 20-25.
Note that for the fields in which both schools are ranked, WI and MN are very similar (Chemical, Mechanical). But on the undergraduate level at least, WI has a deeper field of more highly ranked programs. WI is also more expensive to an OOS student (assuming no scholarship). So I think a lot depends on your planned field and how much credence you give rankings as a proxy for overall program quality and selectivity.
I’ve also included graduate rankings (see below). While grad. school is a whole different ball game w/r/t admissions and academic work, there can still be some spillover from grad to undergrad in terms of reputation and selectivity:
Overall: WI #17; MN #28
Aerospace: WI not ranked; MN #14
Biomedical: WI #24; MN #20
Chemical: WI #8; MN #3
Civil: WI #17; MN #20
Computer: WI #13; MN #21
Electrical: WI #15; MN #21
Environmental: WI #16; MN #19
Industrial: WI #10; MN #42
Materials: WI #16; MN #22
Mechanical: WI #21; MN #16
Nuclear: WI #3; MN not ranked
Hope this information is helpful to you!