Well, since Apocalypse Now is loosely based on Heart of Darkness, it does have other themes, such as the evil of which men are capable. But since war is the ultimate evil, it seems a logical genre in which to explore this theme. Therefore I'd argue Apocalypse Now definitely qualifies as a great war film.

I'm confess I'm not a fan of The Deer Hunter (as one critic famously noted, the wedding went on so long I was embarrassed I didn't bring a present) but I'm with you on Full Metal Jacket, hence the honourable mention. :)