I am so glad that you posted about Brown vs. BU MPH programs, because I am essentially in the same situation. Both programs gave me money and both programs seen really great/align with my specific research interests. However, for me, I am leaning towards Brown for the following reasons:
1. Money: Brown offered me more money. AKA their partial scholarship is per year (assuming that I maintain the grades to not fail out after the first year) whereas BU offers decent merit scholarships--though, at least in my case, it's a one-time thing; not annually renewed.
2. Personal Outreach vs. Automated Outreach: I have received a LOT of emails and a phone call from BU. While some correspondence (usually initiated by me) resulted in a more personal conversation, I'm mostly receiving automated email messages and vague "Come to our school because..." promotions. On the other hand, immediately after receiving my acceptance email from Brown, I received a 100% personalized note of congratulations with information about my scholarship and the entire email was filled with references to my statement of purpose, my personal interests, and offered connections to specific faculty members to contact about shared research interests. Overall, Brown made me feel that they were excited that I was excited to research my particular public health interests.
I totally understand the concern about Brown's MPH program rank/legitimacy. Obviously, as an Ivy, Brown is super impressive and great. But, with that said, their specific MPH program is new and it's hard to figure out how it is viewed specifically within the Public Health world. In contrast, BU is a top ranked program. There is no doubt that BU is currently a leading MPH program and will likely continue to grow in size and prestige.
But, what it comes down to is what program fits you best. For me, my specific research interests align with Brown's faculty and the incredible research resources provided by Brown--and, it's a big bonus being an Ivy with a great reputation and strong alumni network. However, there is no "right" choice when it comes to picking graduate programs. There are pros and cons, ranks and reviews--but you have to simply choose which one is better for you, for what you want to study, and for what you want to do after getting your degree.
In a nut shell: BU has the stronger MPH program and Brown has the stronger overall academic reputation but either school is a solid choice that will help you achieve your public health-related career goals.
Side note: I agree with what others say: both cities can be cold and cranky, but as is the case with any city, there will be things you like and things you don't like. Just remember, you are choosing to head east for the education. After a couple years, you can leave and go back to warmth.