I haven't applied to residencies yet, but I can comment on the type of students in an Ivy League medical school (at least in my class).
I came from a non-ivy undergrad, and chose to attend Cornell because I didn't have any state options due to state residency issues (actually, growing up in Alaska, I didn't even know that Cornell was Ivy League until I applied there, if you can believe that). In addition, my husband is a graduate student in New York city.
My experience has been this: the majority (although not all) of my classmates have wealthy parents who put them in prep school at the age of 3. They attended prep schools all througout elementary and high schools. They attended rigorous SAT prep courses. They then attended Ivy League undergraduate institutions. They then were accepted into their respective Ivy League medical school institutions. I now think that the Ivy League is ridiculously inbred, and I'm going to leave it as fast as possible once I graduate.
I, on the other hand, was lucky to graduate high school without getting pregnant (which is what happened to a large portion of my high school classmates). I attended a very small, very unknown school for undergraduate (the kind where people say "Huh? Where's that?"). To be honest, I think the only reason I got into Cornell is the diversity factor--I'm from Alaska, and there aren't all that many Alaskans in New York City.
My opinion at this point, after two years of Ivy League education, is that Ivy Leaguers are NOT any more intelligent than state school students. In fact, I've been quite disappointed at the general lack of creative thought exhibited by MOST medical students I've met, although many of them are very nice people. Also, I've been appalled at how much these people complain about EVERYTHING--it's as if they expect life to be handed to them on a gilded, ruby-encrusted platter. I now think that the Ivy League is simply a self-sustaining machine, perpetuated by parents who train their children to be good at taking tests.
My point is this--many Ivy League students have been prepped for this their entire life, and thus they don't like to work very hard (again, not all, but a lot more than I expected).
Yes, perhaps Ivy League medical graduates do have more connections, etc...but it's usually with other Ivy League schools, and it's very much a "who you know" sort of thing. Granted, my education thus far has been decent, and I've met a lot of nice people, but I think an Ivy League education is only important if you want to get into the Ivy League machine for residency, your career, etc.
Just my two cents.