Congrats to the OP on having such a decision to make - it's nice to be in that position.
As far as where to go - I'm sure you know that's a very individual choice that will vary from person to person.
I'm an MS-IV at Columbia and am originally from California. I don't know too much about UCSF, but I would suspect that there are more similarities than differences between the two schools. Here are some additional thoughts.
1. Year 1/2 Curriculum
Columbia has mostly lecture in 1st year, then a mix of lecture plus discussion groups with clinical cases in 2nd year. What I liked about the lecture based format is that it gave overviews and structure to the material, and that was nicely supplemented by discussion groups. But then, some of the lectures were boring and not as well tied to clinical material. From some of my PBL-school friends, I've heard complaints that it's hard to see where the case goes in the big scheme of things.
After all is said and done, however, I think all med students learn what they need to. Sure, the 1st/2nd year curriculum will be important for that first 2 years of med school, but I feel that where the larger differences lie is in the clinical 3rd and 4th years.
2. Clinical Years
I've learned a lot during my clinical years from the residents I've worked with, and most residents who work in the Columbia hospitals are motivated, smart, hard-working people. I'm sure the same goes for UCSF. The attendings who I've worked with are the type of people who are attracted to academic careers - some teaching-oriented, some research-oriented, most very efficient with excellent clinical acumen, good role models, but of course there are some egos there.
Clinical sites - probably the biggest differentiator between any two schools. P&S has a mix of sites, though overall, I think the most exposure is to underserved communities, including a large Spanish-speaking community.
At CPMC (where you do probably 1/2 of third year rotations), there are a good number of Dominicans (knowing Spanish helps a lot here), and Harlem Hospital draws more from the African American neighborhoods. About 15% of students go to Native American reservations in Arizona and New Mexico for their family medicine rotations. Other sites are more demographically middle class (St. Luke's near Columbia undergrad campus and Roosevelt at 59th Street near Midtown) to upper class (Stamford Hospital in Connecticut).
So I feel like I got exposure to a mixture of places, but less middle to upper middle class than I would have at, for instance, Cornell.
One more thing about the clinical years, is that P&S is a very surgical subspecialty oriented school, so we spend 8 weeks of third year rotating through ENT, ophtho, anesthesia, ortho, urology, neurosurg. Not sure if all schools do that in the third year. I would also say that there is less encouragement to do primary care type specialties than maybe some Cali schools (not sure about UCSF).
Again, I think the students who choose P&S or UCSF are largely similar - driven, motivated, hard-working (and I'm sure that we can say that about most med students out there). I think there is definitely an East Coast/Ivy League bias in the type of people who select P&S (or are selected BY P&S, perhaps). So I would agree that there is that "aura" of Ivy Leaguedom at P&S. That said, I've met some of my best friends here. I also really respect my fellow classmates, who are, for the most part, some of the smartest, most motivated, multi-talented people I know. (The P&S club is nice for giving different groups of people a venue for developing/sharing their talents.)
Overall, I think most med schools have their spread of personalities (just think about who applies and gets accepted to med school - on average, they're not the same personalities as in the general population!). Some you will like and some you won't.
So this is yet another big differentiator. I wanted to experience something different, and I've really enjoyed living in NY for four years. If you've been in Cali all your life, I think it's definitely an eye-opener to experience the East Coast/New York lifestyle.
5. Residency Opportunities
Both schools have great reputations in the residency world, so I don't know how much you want to count this in your decision.
If you went to UCSF, I think you might have an edge on staying in Cali at one of the UCSF hospitals if that is for sure what you want to do. At the same time, I would assume that residency directors also like to diversify their resident pool somewhat with people from schools outside Cali. Similarly, the East Coast hospitals seem to have a bias for East Coast trained med students. (Just because of the tendency to generalize that "this is a well-trained candidate" based on who you've had exposure to).
If you look at match lists (over a couple years), you can probably get a sense of where the school encourages and prepares its applicants to go.
Best of luck with your decision making process.