Chicago, I'm choosing between Cornell and Columbia, too (well, also NYU and Einstein - got into all the NYC schools and waitlisted everywhere else...go figure!! Guess I'm gonna be a New Yorker...)
My impression, contrary to an opinion expressed above, was that they are VERY different places. Cornell's curriculum is very problem-based; Columbia's is very didactic. Cornell's class, at around 100, is much smaller than Columbia's apx. 160.
CAVEAT: this is all based on my impressions from a couple of visits; you may have entirely different reactions, and my opinions might change with more exposure.
The most overwhelming difference to me seemed to be the atmospheres. The students at Cornell seemed to all know each other and be very close. Because of the small group emphasis of the curriculum (they do have lectures, too, though), they seemed to work really well together. Because they have to make presentations all the time, they all seemed very good at speaking up, contributing their ideas, and having discussions. I admired that. Their grading system is Honors/Pass/Fail, which in this case seemed to give students something to shoot for but discourage cutthroat competitiveness, which I also liked.
My impression of Columbia's atmosphere was less favorable. The students seemed less mature, more competitive, and cliqueish. I sat in on a few second year classes, and watched how people interacted during breaks. There definitely seemed to be people (mostly, as far as I could tell, the older members of the class) who were isolated from the cliques, and like that might be detrimental to their learning (the "I won't talk to you, even to tell you this nifty thing I just learned" syndrome.) I didn't like that people could be marginalized in that way, and it seemed worse there than at any other school I visited.
That was my main concern about Columbia. I also understand from my SO, who did a master's there, that the entire university's administrative bureaucracy doesn't know its right hand from its left toe and moves like molasses in an Arctic winter. FWIW.
The things that worries me about Cornell are 1) the clinical exposure (they kept reassuring us that you really do get plenty of experience at the NY Hospital and the affiliates, but I don't know how to objectively judge that); and 2) PBL sounds great and all, but I'm just not sure that it's the style of learning that works best for me.
Anyway those are just a few of my rambling thoughts. As you can probably tell, I'm really leaning toward Cornell. I'm so nervous about making a decision, though!! Regardless of the differences, they really are both great schools, and I know I'm so lucky to have a choice. Congratulations on having the Columbia choice and I hope you heard good news from Cornell. If you didn't/don't, don't feel bad about it - because they're so small, I got the impression that their admissions process is even more random than most places. Let us know what you decide, and definitely post your thoughts about making your decisions!