So after doing some research ... So, is the USMMA a hidden treasure to those seeking to become airborne? Or is it a vessel (excuse the pun) to train those in all things pertaining to the operation of an American ship? I guess the trouble I am having is seeing how the two can be one-in the-same…
So first let me say the reason you are having trouble seeing how the two can be one-in the-same is because they are, at least as far as your question is concerned, and in my opinion, about as much the same as night and day.
The primary purpose for the opening of the USMMA and it's continued operation as a Federal Service Academy is indeed to train those who attend in all things pertaining to the operation of a commercial vessel and/or shipping company. That is as it was and will likely always be. That said, as has been noted, a USMMA graduate can also opt to satisfy their obligation by going Active Duty Military and some of those opportunities result in USMMA graduates going on to become military aviators.
Further as you note the Naval Academy, and indeed all the Service Academies, including USMMA and USCGA, as well as USMA and USAFA are currently seeing pretty much only the "cream of the crop" enter their doors. They are all great schools and great deals for those who want to or are willing to accept the post graduate obligation to serve. That said, some will tell you, and I would agree, that any small difference in the ease of obtaining admission to USMMA vice USNA you might see or experience, could well be more than made up for by the difficulty experienced getting through USMMA and graduating, especially if it's not a place where you really want to be or where you've decided you have every intention of getting through no matter how hard it is. As with getting in, getting through all five SAs is work and hard, the first/freshman (Plebe) year and the second (Third Class) years at USMMA are especially tough to acclimate to. The academic calendar crams 4 years into three and they are long - basically 11 months long. A trimester at USMMA is basically a 16 week semester at most other colleges and universities crammed into 14 weeks. If you are not mature, your first sea year will be an eye opener and you may find yourself looking for any way out - the easiest being resignation, or you may find yourself with a few short weeks before returning to campus with a tremendous amount of your sea project to get done else facing dis-enrollment.
I'm not trying to scare you I am just saying that regardless of which opportunity you may pursue, any that includes getting through a Federal Service Academy to get to your goal will be hard. Further I am indeed agreeing the primary purpose of the USMMA is to train and equip the world's best Merchant Mariners and the primary purpose of the USNA is to train and equip the worlds best Naval and Marine Corps Officers. If your first choice/life's dream is one or the other of these things than to me your first choice should be pretty clear. Bottom line is I disagree with your statement "... on this matter, it seems as though there is no quantifiable answer." I think percentages are meaningless and easily skewed in smaller populations (USMMA's graduating class is less than 1/5th the size each year of USNA's). The answer is both quantifiable and straight-forward, and keep in mind I'm a USMMA graduate, I'm not saying USMMA isn't a great choice or we don't offer a great set of options and opportunities - it is and it does. I'm just responding to your question and points directly.
Good luck.