I feel a summer internship would benefit someone transitioning from the Military. At the same time, I have to say that the MBA military community is tight and I have noticed quite often that the military guys get recruited first for internships and jobs. They have their own track/network and it is strong. Whatever the magic they have - it works!
P.S. The MSx is a bit easier to get into than Stanford (most exclusive school in the US) and has a different group/crowd, as you noticed does not have an internship and requires starting to recruit almost immediately as you start the program.... many folks prefer a longer transition with an internship. Since you have the amazing fortune of getting into both programs, it may make sense to reach out to Stanford MSx and FT MBA and ask them - let them submit some applications, a couple of essays, and then do an in-person interview, and you can decide which one you will choose

P.S. I would probably choose the complete 2-year experience but that's me, and I did not get admitted to Wharton, Booth, CBS, adn Stanford

so I am definitely made from different stuff.