Harvard is Harvard. There are plenty of discussions on this website that discuss whether or not a name is worth it. Therefore, I think the real question in Boston is BU vs Tufts-NEMC. What does everyone think? Too close to call in my book.
I know Boston anesthesia fairly well. Although I spent no actual time rotating through BU I can certainly tell you there is no comparison between BI (or the other Harvards) and BU as far as reputation, resident happiness, and organized educational experience. Although the clinical experience at BU is very good (they get most of the knife and gun club-while Harvard trauma centers get more blunt) there is next to NO didactics there. The department is run by a large private practice group that $ee$ residents as a cheap $ource of labor. There is no way the residents can be happier at the BU $weat$hop. There is also a large percentage of IMGs. BI may have less OR time than BU but the case mix/complexity at BI is higher. You need to ask yourself, do you want to be stuck in an OR into the evening when you are not on call? Also the patient population at BU is miserable. BU, I believe also trains SRNAs who compete with you for cases.
As far as Tutfs (again-no formal rotation) they also have a SRNA training program. They do some cool cases like liver and heart transplants but I heard their pain clinic was shut down