I got into both last year (UCLA/Caltech) and ended up at Columbia. Initially I got into only UCLA (and not Caltech) along with Columbia. As far as research reputation, *overall* Columbia is probably slightly better than UCLA. However, right now brain imaging is very strong at UCLA. Genetics is probably slightly stronger at UCLA compared to Columbia (with the exception of neurogenetics). Structural biology is stronger at Columbia. The impetus at Columbia was the neuro center, which has a new primate based group that I wanted to work at. Also I dig New York much more than I dig LA. So, in the middle of Febuaray I decided that I'm going to go to Columbia.
Then, at the beginning of march the director at Caltech told me that they will take me. I was completely thrown off the board because Caltech is sort of the crown jewel of everything. Both of my two advisors told me that Caltech has a better graduate school. One of them said, "caltech is really a germ of an institution and one of a kind." The "computation and neural system" CNS program is one of the first and most prestigious systems neuro programs in the country. Bascially every single PI at Caltech from molecular biology/virology to population genetics is a huge name in the field. The only other place I can think of that is somewhat similiar is the Rockefeller University.
The drawback: most of the labs are really large. Yes, you are probably going to work with some Nobel prize winner if you want (I talked to some dude who works for David Baltimore, along with the big cheese himself, at the interview lunch), but you'd have to be within a group of at least 20 or more. Also, Pasadena sucks for social life. even though westwood is awesome (And expensive), most caltech md phd move to pasadena (it is an hour and half from all the cool parts of LA)
So, in the end, my choice was more of my personality. Also, caltech was horrible in that they want the decision in three days. I couldn't even get a revisit. So i guess in the end they didn't really want me that badly afterall. I really wanted to live in New York in my 20s, and I hate driving in LA traffic. California is beautiful, but I don't think it's for me right now. Columbia probably has a better medical school/hospital. Also, right now the Columbia program is much better organized, especially compared to the UCLA/Caltech program. (Basically it's an UCLA MD + a Caltech PhD affair, with no overlap in courses, so the length is amazingly long. Even if you don't do your PhD at Caltech, there is a California State mandate that says all licenced physicians must go for two years of clinical training before getting the M.D. hence, you don't get a fourth year break as you do at Columbia. So the "california" system often tends to elongate MD/phd program, almost always unnecessarily: for more information, read some of the comments made by Duke's MSTP director at intransit.com) As one of my advisor said in the end, it'd probably not matter as much where you go--he trust that I'll be fine anywhere
And I trust that you'll be fine anywhere you go.
P.S. several other people at Columbia right now also had the same choice last year. Hope my experience has been helpful