Long time away from the forum, happened upon this thread, I have input.
To give you background on who I am, I am an NYU med grad, interviewed at Columbia and knew some people at Columbia and considered Columbia for residency (my number two choice) but I got into my number one so I'm not there and I can't admit to personally spending signficant time there. I've talked thoroughly to a couple of big academics who evaluate these things (because I'm interested in an academic career). I'm now an intern at an Ivy hospital that is very competitive and very stellar (I got lucky and I worked hard). I was probably in the top 25-35% of my class. Around middle of the pack first two years but did well during clincal years.
In terms of NYU vs. Columbia as a med school, the generic statement among Academic Doctors is that Columbia is top dog in New York, bottom line. If you want an academic career, if all else is equal or not important to you as an individual, then Columbia should be your choice. By the way, most academcis I've talked to don't really lump the academics at Cornell in the same category as Columbia, but rather think of Cornell more in tune with NYU and Sinai. Maybe its a Manhattan bias, but you don't hear about Einstein being lumped in as the same caliber academics broadly as these other four, but whatever (unless your talking about their renal division or their pediatrics, which are big time).
But broadly speaking, don't get overly caught up in rankings, as the difference in caliber of medical schools in this case really only lies if you aren't a good student and you are at the bottom of your class, but I assure you, if you are that bad, even at Columbia, you won't get a good residency.
NYU is definitely in a great part of the city, easy access to the East Village and downtown in general, while Columbia is a trek downtown (but moderately close to upper west, which is cool, but not as cool as downtown) And don't get too caught up in these Columbia folks talking about their diverse class, by all accounts, the people I met there and knew there were gifted people and had impressive resumes, but this rugby issue and music stuff is so overblown, give me a break. That seems to be all they talk about. NYU has or had at the time, the highest dues (money) paid as part of tuition to student activites of any medical school in the country. We had an extensive international program to Costa Rica that many people went to, and tons of people went to multiple conferences, wilderness medicine electives in the middle of nowhere for a month, electives in Tibet to do craniofacial surgery, etc. It was just a matter of showing interest. Not to mention we had some ridiculous parties at ridiculous clubs and lounges in the city (total top shelf, celeb hangout type places, but I digress) The student body at NYU was definitely not as diverse or impressive on paper en mass as the Columbia student body, as will come with the fact that every premed is obsessed with rankings and every med school is obsessed with resume stuffers, so the result is obvious. But in general, it was a young and fun group of people who studied hard and played hard.
However, if you are an average to above average medical student at NYU, the sky is the limit for your career. I literally know med students in my class who were not AOA, who had the residency director at Mass General call them personally several times encouraging them to go there. (I'm using mass general as the gold standard of residencies, which it isn't always, but that leaves an impression on you prestige seeking types...not excluding myself.)
If you just liked NYU more than Columbia, go there and have no doubts. I know of at least 10 people in my class who chose NYU over Columbia (I couldn't believe it, because I was one of those premeds obsessed with rankings and I would have gone to Columbia if I got in, but I did not). They cited that they just felt more comfortable at NYU or they liked the location or student body better or they had a particular interest in a particular program or that they LOVED THE IDEA of working at Bellevue. As much as the above Columbia students like to compare NY-presby to Bellevue, this is one feather in their cap that NYU has that you really can't deny. Bellevue is the oldest and largest public hospital in the United States and it is the place where the **** hits the fan and you are there to be covered in **** as a medical student. Talk about international health, its all right there in Bellevue, no contest. Of course, NY-Presby is far superior to Bellevue in many things and it is a very hands on rich in clinical stuff hospital and it has much better specialized surgical care, but its not Bellevue.
Bottom line, you make your experience in med school meaningful and your future bright by being proactive about the direction of your career, seek out things and you'd be surprised at how much interesting stuff and important stuff you will be exposed to. Don't just study, because success in your career will also be determined by your experiences and connections, as the grades are a big blur unless you are really at the top or the bottom.
In general, Columbia has a more academic millieu to it and highly specialized things and research is broadly richer at that place, so its a tough place to turn down and its really one of the top handful of academic places around, but if you are into student body, extracurricular stuff, location, international health, or great clinical training, Columbia is not the better choice, it may be equal or comparable, but its probably just a matter of where you felt most comfortable and you are not hurting yourself by choosing NYU, I promise.
Sorry if this offends anybody just hoping to get into a med school, the general lesson here is that any med school offers you a million opportunities to succeed, some are just more in your face than others.