Stereotypes that have some truth to them: Colgate is a very greek, party hard, preppy pre-professional school. It is also extremely rural and isolated. The town of Hamilton is tiny and it is hours to anything else. A large percentage of the class aspires to Wall Street careers. It is more politically conservative than Middlebury. Sports are D1, which is intense.
Middlebury is more intellectual/academic as opposed to preprofessional. Many students go there for foreign languages, international diplomacy studies, and so on. Middlebury does not have frats. Like Colgate, Middlebury is rural and isolated, but the town is much larger than Hamilton closer to other colleges/towns. It is more politically liberal than Colgate. Sports are D3 but the running team is always strong.