(This is just a cut and paste of what I wrote in the Allopathic forum for the same question)
I interviewed at both schools (ended up going to the University of Michigan) and here's the impression I got from the school/students -
Columbia is first rate when it comes to academics and research - much better than NYU in my opinion. The curriculum in both schools is pretty traditional (Dr. Frantz of Columbia didn't believe in the PBL "fad"). Columbia, while not in a bad neighborhood, is so far uptown that there really isn't much there. NYU is closer to the city's attractions. NYU's Bellevue Hospital is famous for allowing 3rd years to have much more responsibility, since they are badly understaffed there. Columbia students have a reputation (whether or not it is deserved I don't know) for being snobby - if true, not surprising since Ivy Leaguers are vastly overrepresented there. Despite that, I think most would choose Columbia over NYU without much hesitation - the facilities at NYU Med leave much to be desired. Columbia's administration is notorious for being indept - during graduation one year, the student speaker joked about how she still didn't know who her advisor was. When I was there, they scheduled our interviews during the time we were supposed to get a tour....