It really depends on your career goals I think.
If you're into the name, obviously it is hard to beat HMS. If you want to be in Boston and kinda have a good chance to stay in the same system for your residency (stay in Boston at any of the HMS affiliated hospitals), then HMS is a great choice because they retain a lot of their own students (highest rate in the country, I think). I would say that the feel of the school is important, too.
On the other side, if you want more flexibility financially as a physician, then the full ride is likely the ticket. The loans vs not having to pay anything really puts you in a tough spot...if you want to be able to do whatever you want in medicine, then no loans is the way to go. If you want to do work in underserved areas, abroad, practice medicine at a little more of a "leisurely" pace where you REALLY spend a lot of time with patients or even start your own practice, the no loans is the way to go. I'd like to think most of us have gone into medicine for the excitement of medicine and helping humanity and those in need, but it is foolish to ignore the financial implications of getting a medical education and supporting yourself as a physician. I can imagine that despite doing their best, physicians are plagued by the pressure to keep their practices afloat or perform to the financial expectations of a healthcare employer (hospital/clinic) and I have a feeling that it affects their happiness and even their performance as physicians...it is an unfortunate, sad scenario.
So, in short if you like the name and the opportunities that come with it and are comfortable with being a little leveraged in terms of how you practice medicine, then HMS is your place. If you really are averse to the pressures of money and want the discretion to practice medicine your own way, then go with the no loan school. It is harder today for MD's to "hang up a shingle" and start practicing in their own facility because of financial constraints, so institutional medicine is usually the choice. But the people who seem to be able to go into private practice off the bat are those who have little to no debt. Plus, I feel like getting a job in institutional medicine hinges a little more on your "pedigree" whereas your ability to go into independent private practice immediately after residency does not depend on those same things as much.
I don't pretend to know all of the answers, but this is just my two cents. I really hope this helps. I always like to hear other perspectives from other students so I figured I would do the same.