In terms of research/academics though, hands down Columbia. Brigham is pretty weak that way i thought. Sure, you can go do research at MGH or MIT but it's not the same as working on anesthesiology-related research with your own attendings. Plus the mentorship wont really be built into the program like it seems to be at columbia if that's what you're interested in (I am). I also thought the BWH program seemed to steer residents away from an academic career, or in any case, didn't really seem to encourage them to do academics. I thought Columbia was much stronger that way. In terms of a supportive environment by the PD, assistant PD, and chair, though, Brigham wins--i dont think any other program comes close to the quality of that team and the care they have for their residents. I cant really comment on hospital environment. I did a 2nd look at brigham, didn't get a chance to do so at Columbia. The ORs at the brigham are very new and nice looking. The impression i got re: the faculty from the very limited exposure i got at each place, I actually thought in general the faculty at columbia tend to have more confidence in each resident's talent. At brigham i sensed a bit of a vibe that certain residents get "demoted" while others get "promoted" so to speak, based largely on first impressions. Maybe it was just the particular attendings I happened to come across at each place. It was a gut feeling, and could very well be inaccurate.
I was actually REALLY impressed by the resident camaraderie at Columbia. the brigham residents were really great, but the residents at columbia seemed extremely down to earth, sincere, collegial, and pretty darn cohesive i thought. Maybe i just felt like i fit in slightly more with the personalities at columbia, dont know.
I did overall like both programs very much. My family is in boston but i actually ranked columbia higher because there I felt a lot more reassured about opportunities and mentorship towards the type of anesthesiology career I envision for myself.
sorry i know this didn't really address your specific criteria, but differences in those particular areas are really gonna be nitpicking. The 2 places definitely seemd to have different overall focuses. Brigham seems to aim to train very excellent private practicioners (even those that do fellowships--pretty high powered ones--seem to end up in private practice in the end). columbia seems to make a large effort to attract candidates who want to be anesthesiologists-scientists (many do go on to private practice, but there is a lot of support and encouragement for those interested in scientist training.) Honestly i dont know that the brigham-harvard name carries that much more weight than the columbia name. Mass general maybe, just cause that's where it all started (in some ways). Columbia has tons of history and ground-breaking too.
As someone already alluded to, the decision all comes down to your own individual preferences and what kind of career you want, where you feel you fit in best, which city you prefer, etc. Both are top notch programs. No two (even great) programs are alike though. On interviews i recommend instead of comparing the "work hours," etc, get a feel for what unique qualities each program has and make your decision based on that. Of course that means you should kind of have a general idea of what kind of a career you envision for yourself ahead of time.