UW hands down. Academics much better at this large research U. You will find your peer group in Honors classes- great program. Academics are great at UW- so many top tier rated grad programs. This means opportunities for honors undergrads as well.
I understand wanting to leave home. If at all possible live on campus (Res Halls). I really did not want to go to UW eons ago coming from a Madison suburb but found the campus to be a world apart from the rest of the area. A friend walked from home to classes and missed out on a lot of evening/late night time with us. Vastly different to be a part of campus than to take a class there.
Just because a school is small and private does not mean it will have as many top tier students. UW has the regular above average college student and the top tier students who populate the honors classes and who are as smart as elite school kids. Also- will Carleton have the majority of STEM minded students, or will those interested in sciences just be premed? That is different than being in science for its own sake (I was a chemistry major, then chose medical school). More than one of any intro class to choose from.
Those intro courses will NOT need to be as you describe. Look at the Honors math, chemistry, physics and Biocore sequences for example. Several options for all breadth requirements. See the recent thread about biology majors at UW and my long premed post. Intro level courses at UW are not typically general survey courses but delve into more specific subjects.
Your big question is do you want a small LAC or do you want a top tier research U. I would definitely opt for the opportunities at UW since you want the sciences.
btw- if you go the medical school route you will face tons of memorization there. A pain, but necessary.