like trout, i'm biased cause i've alredy made my decision to go to columbia, but here are my thoughts because it came down to the wire between these schools (more just stanford and columbia, but that's cause i went to yale undergrad).
i think that the curricula are more similar at stanford and yale - they are both really flexible and many people graduate in four years. there is a lot of money for going out in your own direction. the curriculum at columbia is far more traditional, but has perhaps the best hospitals. also, with that tradition comes an enthusiastic support of the medical school that gives columbia a different feel than any other school i visited. somehow, everyone there seems convinced that columbia is THE BEST. which makes a whole lot of talented people feel driven to do their own best. the energy is tremendous, and i anticipate the opportunities being limitless as well.
in terms of quality-of-life stuff, you are dealing with three different places as well. all three schools have reputations for having really happy students. but that's partly because the people who attend generally chose the schools they want to attend. so you have to wonder about things like class size (stanford - 86, columbia-150, yale somewhere in between), location (suburbs, small city(but new haven is awesome - don't turn your nose up without going!!) or the greatest city on earth.)
basically, this is a decision that you are LUCKY to be making, so take your time with it.