I don't know about med school but can speak about going to a prestigious undergrad. I think that it is easy to get lazy/complacent at a top school because you figure you've made it, you're in this elite club and don't have to try as hard. I know a lot of students who got to harvard and just didn't shine, just were happy to scrape by without really striving for greatness because hey, they were in and they got good jobs when they graduated because of the name. I guess some people see this as a plus of going to a top school but I see it as a shame. i'd like to think that this didn't happen to me and i know it didn't happen to a lot of people but it does happen pretty frequently, it seems. another part of it is, you figure that its impossible to be at the top so you strive for mediocrity instead whereas in high school it was easy for most of these people to be the big fish in the small pond. if you want to be the big fish, you better be a whale at a place like harvard if you want to stand out. personally, i loved it and just did my own thing while there, not really worrying about other students but i know not everyone was like me.
also, for the rest of your life, every time you do something dumb or don't know some random fact you'll hear "but you went to Hahvahd.....!!!"
the good parts of going to harvard far outweigh the negatives in my mind though.