JPJ:
Probably the best way to directly answer your question succinctly is this:
U.S. News and World Report Ranks" U.S. Merchant Marine Academy Second Best Public Regional College; 2014 rankings offer data on nearly 1,800 schools see the following link:
http://www.usmma.edu/about/communic...us-merchant-marine-academy-second-best-public
As already described as with each of the other four federal academies, USMMA has its own unique mission and as such is slightly different than the other academies.
Also as already addressed I suspect the way you asked the question will generate at least a little consternation in some of the response and you might want to follow-up with a little further explanation as to the nature and reason for your question. Many may see it and react without looking further to see that you have 36 posts on this forum and are a truly interested PC actively pursuing and considering multiple potential avenues to a sea going commision.
That said I too tend to be a little overly direct and blunt and am curious - have you already confirmed that the medical condition that disqualified you from USNA and a an NROTC scholarship either will not disqualfy you from USMMA or have you cleared that issue and are all of the earlier issues preventing you from getting into USNA and/or an NROTC Scholarship no longer an issue? Further if not have you verified that if that condition doesn't recur or exacerbate during the next four years if you get through another four year commissioning source USMMA, VMI, etc that you are pursuing - you will be able to commision and it won't prevent you from doing so then?
I'm not trying to stir up stuff - I just would hate to see a young man or women go through four years at any of these difficult programs only to find they never really had a chance of succeeding in attaining their ultimate goal. None of the options you are considering are easy to get into and they are all even harder to get through.
That said, as you know on all these forums we all like to thump our chests and say our Alma Mater is the best the other option is less than the one I took, etc. But the truth is we are all arguing about different degrees of excellence IMO as I believe the above referenced USMMA kudos illustrates.