I currently live in Minneapolis and lived in Milwaukee for 6 months doing a co-op so I have knowledge of both.
At first, I really didn't like Milwaukee but I have to say it grew on me. From having attended UW, I really like the whole Wisconsin drinking/brat/cheese curd type culture and having it in a big city like Milwaukee compared to Madison was pretty cool. With that sad, when I was in Milwaukee I always felt like if I took a wrong turn, I was just blocks away from being in a bad area no matter where I was downtown. Milwaukee is just a couple hours south of the Door County area up by Green Bay which gives the opportunity for outdoor activities. I lived by UW-Milwaukee which is a nice area and I did take the bus around pretty frequently but I wouldn't say it has great public transportation.
I love living in Minneapolis. It's much more of a modern, professional city in comparison to Milwaukee. Combined with St. Paul, I feel like it has much more diverse options of things to do than Milwaukee would offer you. Minnesota offers similar outdoors options with all of the lakes up north. Duluth has some great rivers with waterfalls that I love hiking along. Minneapolis does have a light rail that the state is continuing to invest in. It's not very extensive though so you still end up driving to it to take it downtown. Overall, from my experience, I don't think either city has great public transportation that makes it really easy to get from the suburbs to downtown.
If you've got other specific questions that I can try to answer just let me know.