The argument about people in different departments at Columbia competing against one another for the same jobs is one that I hear a lot on quantnet and think people really put too much emphasis on. Yes, obviously they are and that sucks, but it's not like Cornell grads aren't also competing with those same people. So let's say 5 Columbia MSFE students, 5 Columbia MSOR students, 5 Columbia comp sci students, and 1 Cornell MFE student are competing for the same job, I think people in this forum overestimate the power of that different Cornell name sticking out. Sure, it makes a difference but in most cases I'd think it was pretty marginal. I have looked through stacks of undergraduate resumes for applicants to summer analyst and full time analyst programs at my bank, and the vast majority come from the same schools. When a resume comes up that says a more unusual school, I don't give it special consideration unless I'm doing it subconsciously. And, yes, I'm talking about the more unusual schools which are on par with the usual ones (when a less strong unusual school comes up I need the rest of the resume to be even more impressive to make up for it). Granted this is not the same applicant pool nor the same sort of position looking to be filled, but this has been my experience when considering recommending resumes for interviews. I don't have quotas to fill for number of students to interview from each school. If I wanted to, I could in theory only choose applicants from one school.
What will make a difference as bullion said above is if there is a targeted career staff that is truly working its balls off to place its students. I did not feel as if we had that at Columbia for any of those programs. Obviously we had career services but I didn't feel as if they were bending over backwards for us. If a program truly has that sort of service, that would definitely be a differentiating factor.
Finally, and this is the more generic bit, I think it depends on what your goal is after you graduate. I'm sure there are positions for which the hiring managers look for particular things. For example, if you what you wanted was to be an equity derivatives quant specializing in developing new pricing models for structured products, I'd imagine most hiring managers will be looking for relevant coursework and they might even have a short list of programs they are familiar with and wish to hire out of. That's obviously a ridiculously specific example but you see what I mean. If you just want to get a regular trading or structuring position at a bank, it's more powerful to have a better brand name school on your resume than a particular program.