Well, people, I am totally, totally stunned.
You all basically confirmed my suspicion: First, that women seem likely to choose different movies from men, and, second, American war movie consumption is heavily slanted toward Hollywood movies. (On various national holidays, American television will trot out the same few movies, over and over, like The Longest Day or A Bridge Too Far - which, if nothing else, proves that it's smart to use a lot of big-name actors in epic war movies.)
I suspect a third thing may be true, that women are likelier to choose movies with a strong human content - i.e. with an emphasis on character and personal stories, not just fighting. But I can't be sure, because so many of the titles are unfamiliar to me.
And that was my real shocker, so many unfamiliar titles. I've had not only the benefit of living in New York City, a city with possibly the most access to old films in America, but also own a raft of film reference books. So I know about all kinds of movies that I've never seen. I never expected to see so many new titles. And such a breadth! It's not just that I haven't seen them. It's that I've never seen them running ever, anywhere.
I'd really like to post this same question now in the two American forums I regularly use, just to compare the answers. I have the feeling that the answers would cluster mostly behind a far smaller number of films - Great Escape, Private Ryan. And - ha! - maybe you ladies could swoop in afterward and educate them.