I want to thank everyone for the input. To me, the ideal situation is to have both the brand name and the knowledge like UC Berkeley, but that's hard to get. The dilemma is when you can have only one of them.
I personally strongly believe(rightly or wrongly) that unqualified candidates from brand name schools will get more interview calls than qualified candidates from less-than famous schools. I am speaking from my experience because I am working now and am involved in the recruiting process.
I went to a decent but not-famous school. When I passed all the interviews to get my first job, the VP and supervisor told me that they didn't expect to find any qualified candidate from my school. So they arranged 3 rounds of interviews for me, as supposed to the normal 2 rounds. Of course whether one gets through all rounds depends on his/her skills. But brand name really helps in getting that first phone interview invitation, and having more first chances is a huge advantage.
I am not saying UCLA is not brand name or Columbia MAFN is not a good program. Personally, I much prefer the structured curriculum and faculty at UCLA over the math-oriented MAFN, but I think most people will agree that Columbia has a much bigger brand name than UCLA. Especially because it has a huge undergraduate population, getting into UCLA just doesn't seem impressive to any outsider who doesn't know its b-school is ranked #7 in finance. Even one of my recommender thinks Columbia is "far better" than UC Berkeley.
By the way, I am not picking on these particular schools, but just using them as examples.