If you intend on majoring in Neuroscience and/or CS, then Michigan may actually be slightly better than Chicago.
How come Michigan is cheaper? Are you a resident of Michigan or did you just get a nice scholarship? Either way, Chicago and Michigan are peers, so if Michigan is significantly cheaper for you, and finances are a concern, I would definitely recommend Michigan.
Of course, if your parents can afford the different with relative ease, then I would go for fit. Although both universities are truly exceptional, they are very different. You should be able to decide which school is better for you on your own.
For example, Chicago is slightly more intellectual and intense academically, Michigan tends to be slightly more laid back. Michigan is larger and is probably more intellectually diverse than Chicago. At Chicago, most students major in the traditional disciplines. At Michigan, students also major in Music Performance, Visual Arts, Nursing, Kinesiology, Engineering, Business, Public Affairs, Education etc…
Socially, Michigan will have everything from the highly intellectual and serious types to the wilder party types. Many students love the arts will spend most of their free time engaging in some sort of intellectual activity, yet there is enough interest to fill a football stadium to capacity on any given Saturday and 15%-20% of the students belong to Fraternities/Sororities etc…Chicago will probably be less diverse in this respect as well.
It does not end there. Chicago only has 5,000 undergraduate students, compare to Michigan’s 28,000. Classes, particularly early on, are going to be smaller and more intimate. Michigan has the resources to handle its size well, but you will still have very large intro-level classes. Chicago is obviously located in one of America’s largest and nicest cities. Ann Arbor is your quintessential college town, quaint, pleasant and fun.
Like I said…two exceptional universities, but very different. It should not be all that different for you to choose. First establish whether or not you can afford Chicago. If you can, go for whichever school best fits you personally.