Hi--I interviewed at both Vandy and Chicago. I was accepted by Pritzker, and was waitlisted by Vandy.
I may be able to provide some insights into Pritzker, because I have two friends on the faculty there.
Vandy seems to be very very conservative. Chicago seems much less so--even given the reputation of their other graduate schools.
Vandy is GRADES GRADES GRADES--from day 1, you are given As, Bs, Cs, etc. They are also in class ALL THE TIME for lecture.
Chicago is pure Pass/Fail--meaning, not even like Northwestern's curved p/f, where the mean is set by the curve. At Chicago, they will lower the typical 60% pass point if everyone does poorly.
Vandy's anatomy class has about 5-6 people per cadaver, and you don't have the chance to do all the dissections. At Priztker, there are only 4 students to a cadaver, and you get to do all the dissections. Chicago's anatomy labs are BRAND SPANKING NEW and right next to an advanced computer lab dedicated to anatomy study. The anatomy labs were designed for maximum student comfort--they have three separate lockers (one for their books, etc; one for their clean clothes; one for their dirty anatomy clothes).
Chicago has an awesome interdisciplinary focus, where you can design research projects with MDs and PhDs. They are really open to student ideas for research. (I came up with my own, and I was able to do it EVEN THOUGH I WASN'T EVEN IN MED SCHOOL!!!) I can't comment on Vandy's research strengths, but their undergrad/grad school is not as strong as Chicago's, IMHO.
Chicago has top 10 law and business schools where you can get a dual degree REALLY EASILY. Vandy doesn't have top 10 law and business schools.
I love Chicago/Pritzker. I'm probably not going to be attending, for other personal reasons. NOT because of the school.
Frankly, I think Chicago's match results are better. I think that Vandy's students are really hurt by the grades they get--a Vandy "B" is not a Hopkins "B"--that is a cruel but I believe ultimately realistic statement. But at Chicago, you get a P, and that's frankly harder to distinguish from other Ps at top schools.
Nashville has great music, but the city is just not kicking like Chicago is--Chicago is the third largest city in the country, has a great public transport system (which Nashville does not), and has a great music scene as well.
Chicago also has Northwestern Feinberg, and I'm sure if you wanted to do rotations through NUMS affiliates (like Rehab Institute) you could. There are just not as many TOP TOP hospitals in Nashville as there are in Chicago... Chicago has the Rehab Institute, Children's Memorial, you name it. Pritzker itself has great great hospitals, and I had the strong sense that Vandy's hospital was much smaller and less of a complex system than Pritzker's.
The students that I interviewed with at Vandy were not as interesting and diverse as those I met at Chicago.
The Vandy tour guides were not that hyped about their school. They came out and said that the lectures kill them, and that they teach toward the boards. Which I guess is good, but it's not like Vandy kids are getting matched at totally awesome places.
That's my two cents. I could type more, but I won't, 'cause I'm getting tired.