I have to disagree a bit with the above poster.
Boston is busy like many big cities, but I don't think it's dramatically harder than any other academic programs in terms of workload. It's certainly no NYC. Also not sure what they're basing their impression of Tufts in terms of "rule over the place in clinical training".
MGH/BWH: Large HMS affiliated programs. As expected, they are very competitive and match to fellowships well.
BIDMC: Also HMS affiliated, though for some reason a bit smaller than the above. Don't know any people in this program personally, but they appear to match well. I'm curious what the above poster's specific issues are. BIDMC's reputation is "Harvard with a heart", and are allegedly chiller than the two above named HMS programs. From what I've heard, that reputation is largely true but small sample size, mainly from medicine.
Tufts: Trend of being IMG heavy, with a few Tufts grads mixed in. Smallest of the academic medical centers in Boston, and the smallest associated residency. From people I know at the hospital/medical school, neurology is not particularly strong compared to other departments. For a relatively solid medical school which has otherwise competitive residency programs largely filled by US grads, I'm not sure why this is the case. If interested, patient population has higher percentage of Chinese patients than other programs in the city, as it's located in Chinatown. About a mile away from BU/BMC.
BU/Boston Medical Center: I feel most people in the city would place it somewhere between the HMS programs and Tufts in terms of competitiveness. Almost all US MDs. BMC is the safety net hospital for the city and is located near services for patients with SUD, homelessness, etc. On one side of the hospital you have Boston Healthcare for the Homeless as well as a large homeless encampment a few blocks over and on the other, you have multimillion dollar brownstones. Per people I know there, safety around the hospital isn't too much of an issue and residents seem happy. Also large proportion of non-English speaking patients, and residents also staff the VA. New department chair sometime in the last few years from Yale.
UMass: Not in Boston - it is in Worcester, MA, about 45min - 1 hr away. UMass is the tertiary care center for central MA, and parts of CT, NH. Less competitive than the Boston programs, partially because of location. Not sure how I would rank relative to Tufts. Trend with a mix of UMass grads, DO, IMG. From people I know at the medical school, the residents also seem happy, looks like a decent match list. Students interested in neurology at the medical school also match well, if that reflects on the quality of teaching from faculty/residents. Lots of basic science research on campus, including the physician researcher who discovered the SOD1 gene associated with ALS.
I know much less about Baystate (Springfield), Lahey (Burlington), and St. Elizabeth's (Boston).