Can you explain which one is correct or if both are correct, under which scenario one is more suitable than the other? I have this doubt in general, when to use nouns as adjectives or possession like in this example. Can you give me some pointers?
"Men's" is idiomatic.
The players on the U.S. Olympic men's basketball team never doubted they would be standing on the gold-medal platform....
Either "men's" or "men" would be possible in terms of basic English grammar, but in practice, Americans almost always say "US Men's (or Women's) ___ team." For example, US Women's Gymnastics Team, or US Men's Olympic Swim team.