CMU vs UW-Madison

I’m currently trying to decide between CMU and UW-Madison. I plan on studying engineering - probably chemical but I’m also possibly considering mechanical - with a possible minor in CS. Can someone give me pros/cons of each school? A couple things I’ve already considered: a) I live in Madison and while I love it, I might prefer to go somewhere else for college b) CMU is much stricter than UW as far as transfering between schools/changing your major dramatically c) CMU is more expensive than UW.

Any thoughts are greatly appreciated!