Which Hollywood military film is the closest to "reality" in your opinion?
Band of Brothers (the HBO series) was excellent. But that had a lot of written history behind it, several living experts, and was a Tom Hanks production. So you should expect quality and near perfection.
I'll have to think about this one, because a lot of the films end up being characteurs. But I will agree that Saving Private Ryan did an excellent job in many ways, especially viewer immersion during the beach landing scene. The sounds and visualizations made you really feel like you were there on Omaha crawling through sand, mud, and body parts.
EDIT: I found a list so here is the link and some thoughts:
http://www.mrqe.com/lists/best_military_movies
The Hurt Locker while mostly about Jeremy Renners' character's ego was surprisingly good and earned every accolade it got. Even lending to the notion that this guy worked out side of the box, I can't imagine many EOD types being upset with authenticity or tactics. I'm sure everything wasn't text book, but that was the point, this cat was rogue but effective.
Black Hawk Down was so real and good that when I saw it in Nashville with a bunch of 160th SOAR and 5th Group guys everyone left the audience rattled and crying. And I mean, EVERYONE. I would not be surprised if many of these guys were there or knew people that were. 160th SOAR had a major role in the incident, the book, and the movie.