One thing you should keep in mind is what region of the country you plan on doing your residency in, simply because the location of your medical school will matter much more than the name of your medical school when all is said and done. That's especially true when considering schools like these, because both Vandy and UM are terrific programs and will give you the same opportunities to succeed provided that you'd feel comfortable and happy at both.
I'm a 4th year at Michigan and was accepted at Vandy, as well. If it makes any difference to you, I haven't had any problems getting interviews in the South or East coast in a very competitive specialty, however the West coast has been pretty tough. I would imagine that this would hold true for students at Vandy, as well.
My main reasons for choosing Michigan were the following:
1. The most important element of your education = clinical medicine (i.e. 3rd year). In this regard, it just doesn't get any better than what we have at Michigan. Great faculty across the board that are approachable on the whole. Also translates to big names when it comes time to get LORs.
At your level it's hard to evaluate this stuff because all you're familiar with is studying in a library and taking some exams. That's really not at all what being a doctor is like, and the people that work around you and with you will determine your happiness to a great extent. But speaking of exams...
2. The first two years. They're awesome at UM. Strictly P/F, just need a 75 to pass. And don't worry about busting your ass for Step 1 at this phase - most of what you learn in the first two years of medical school isn't useful. You just need to get through it and learn what you'll need for boards, and Michigan does that incredibly well while also giving you plenty of time to enjoy yourself. Everyone here does a ton of stuff outside of med school. While things might have changed at Vandy since the time I applied, I didn't get the impression that the first two years were as laid back there.
Because it's totally P/F at UM, you have zero competition with fellow classmates. Everyone's out to help everyone else. I cannot think of a single instance of anyone screwing anyone over in the entire time I've been a medical student here.
3. Ann Arbor. Seriously, I came from a big city for undergrad and was worried about the whole midwest thing, but I have grown to really like it here. There might not be 25 different sushi restaurants to check out, but there are a handful of good ones. There's plenty of stuff to do outdoors in terms of parks, trails for running and biking, great golf (that's also cheap). The winters do suck. No doubt about it. But spring, summer, and fall are that much sweeter for it (and seriously, they're great).
4. Gut feeling. People are just nice here. Ultimately, I feel like this is what really matters at the end of the day, because if you're not going to be happy somewhere, it's not worth losing four years of your life over it.
I have no incentive in you choosing to come to Michigan rather than going to Vandy, and I certainly have nothing bad to say about Vandy (terrific program on the whole), however I can honestly say that I would choose to go to Michigan all over again.
Good luck in your decision and congrats on having two (or more) great acceptances. 👍