I have visited both and know them quite well. I think the answer as to which is better depends heavily on your point of view. Let me try to clarify:
1. Academics (MS 1 & 2): The differences are quite minimal. Both remain quite didactic in their pedagogy and have long days. BU starts clinical a bit earlier, I believe, but Tufts has a more well developed dr-pt society class. The dept of family medicine (which typically has a hand in these classes) is stronger and less apt to dissolve at BUSM. Tufts may have a slight edge in how students are treated (i.e., how 'nice' everyone is) and BUSM has an edge in incorporating topics like functional anatomy into the curriculum.
2. Clinical years: If you are interested in primary care, emergency medicine, geriatrics, or pathology, there is little doubt that the clinical experiences and resources at BMC are much better. BMC is a level I trauma center that receives over 70% of the trauma cases in the city, has the Mallory Pathology center, runs the Geriatric home visits program (in which all 4th yrs must take part) and has a strong tie not only to the community health centers, but also to providing care for those who are uninsured and underinsured. Tufts has the advantage in certain internal medicine specialties (such as cardiology, nephrology, and the like). Surgery is good at both institutions, but for different reasons. The principal teaching hospitals are also quite different in the populations they serve and thus in the types of cases one will see during clerkships.
3. All other: Price, call them equal. Neighborhoods: I personally dislike the crowding and smell of Chinatown and I wouldn't live there. BUSM isn't is a terribly fantastic neighborhood either, but few med schools are. Finances: BU appears to have slightly more low-interest loans, but they'll both cost you about $40,000 a year. The administration at both schools seems to be similar-- financial aid offices and registrars are not known for being "user-friendly" anyway. On another note, the USMLE pass rate at BU was about 99% this year while Tufts was lower (I don't remember the exact figure).
In the end, both are really strong schools. I've been to an ivy league school, so I have something to base my thoughts on and I am convinced that for med school almost any school in the top 50 or so offers a similar education. It should come down to where you feel most comfortable, how you perceive the students, availability of faculty, etc. You can check out the match placements to develop a sense of where students typically go. You are indeed fortunate to have 2 solid choices, either of which will provide you with excellent credentials going forward. Go with your intuition, revisit if you can. Good luck.