Chem E at UW is a top department, typically in top 5 though seems to have dropped to 6 in one recent ranking.
With in-state tuition at UW, I’d take the UW acceptance and don’t look back. Michigan has the stamp of approval of being a “top” public, but if you look at specific departments, head-to-head, there is often parity between them, and there are departments where UW is better – including Chem E. Regardless of how people on the street think of the two schools, UW is going to be very well known among employers as a top Chem E department. My UW student has many friends in Engineering and they are hard working, very smart students.
Yes, UW has a reputation as a party school, but there are many many hard-working kids who are not hitting State St bars 5 nights a week. Madison is a great city, a “foodie” capital, with big farm-to-table movement, plus it is the state capital so there is lots going on.
Congrats on a great transfer result, you must be a very strong student!