Its a tough call. Both hospitals are about equal when it comes to prestige. But I think i would rank BID over Tufts. To me, Tufts is just an "ok" place to train - Don't get me wrong though, it is an excellent hospital with great clinicians. However, the general consensus is that people aren't very happy there. Just look at how many Tufts med students stick around for internal medicine there. There's like 2-3 per intern class. You could probably say the same for BID, but the truth is, Harvard students have much more to chose from than just one tertiary care center.
With the exception of the General Surgery residents at Tufts-NEMC and a very few OB and Psych residents; I have not found the residents at Tufts to be particularly happy or competent people. Granted, I don't really know any IM residents, but it is generally known among Tufts students (I'm one) that NEMC is not a great place to do your IM rotation (Faulkner and Lahey are usually the most popular sites). I would go with BID hands down; better reputation, broader range of opportunities, more exposure to trauma in the ER (the NEMC ER blows). I got to shadow a BID IM in his clinic for one of my 2nd year selectives and he was awesome! I would love to go there for residency, but doubt I'll get the chance due to mediocre stats (haven't had my medicine rotation though).