At the end of the day, the one of the best metrics would be to see how satisfied students were with their medical education experience and, ultimately, residency match outcome.
NRMP Match data (page 41) shows that
51.6% of US seniors received their #1 choice. The "best" medical schools will likely be those that have the highest standard deviation from the mean. Remember, #1 choice doesn't mean the most competitive or geographically alluring destination, but it reflects a combination of factors that each student finds to be most important. It would be incredibly useful to see the breakdown for individual schools, along with surveys on other satisfaction parameters including whether or not they even interviewed at what would have been their possible #1, 2, 3, etc. choice. However, this information is rarely made public. For what it's worth, my school, internally, reports a 76% match to students' #1 choice.