Many aspiring premeds just default to majoring in biology. It’s not necessarily the best choice - choose a bio major only if she’s passionate about the subject and about studying it in more depth than one strictly needs for pre-med… and also if her Plan B (if not med school) is grad school. Employability with an undergrad bio degree is not great.
One huge advantage of CWRU is their open door policy re: majors. She can explore and choose any major she likes, without barriers to entry.
UMich is better than most large state flagships with regard to major flexibility, but still not as flexible as Case.
UMich is unusual in giving any need-based aid at all to out-of-state undergrads. But this funding goes only to low-income students. If you were in this category, you would have gotten more aid than you describe from Case. So you should expect to be full-pay for UMichigan, for an out-of-pocket that’s nearly double what you’d pay at Case.
As others have stated, there’s no meaningful difference in the overall academic quality between the two. There are pros and cons on both sides, but nothing that could make one worth double the cost of the other.
Most people, especially high school students, are ignorant about colleges. My daughter went to Rice, a top-20 university by most rankings, and most people at her high school hadn’t heard of it. She was variously asked why it was named after food, whether it was an ag school, and whether it was as good as UC Davis. (No shade toward Davis - great school - but Rice is vastly harder to get into.) Tell your daughter that when she gets there, everybody will have heard of it. CWRU is a phenomenal choice for an aspiring doctor, and she’ll have money left over for med school - win-win.
You have an opportunity right now, before you get your (no) aid package from UMich, to tell your daughter what you’re willing to pay for her to go there. Perhaps pick a figure halfway between CWRU’s price and the UMich full-pay price. If a miracle occurs and money appears to make this possible, fine - but it almost certainly won’t. She may at one point have expected you to be willing to full-pay, but the world and the economy have changed since then.