I’m not sure I can pick one. Each one is a product of its time; KH has a tighter script and some great setpieces, but 3K is more sympathetic to those affected by war and is filmed in a much more inaginative manner. Both have some great performances, IMO: in KH, Sutherland’s anachronistic Oddball, Rickles’ Crapgame, the supporting players (including Harry Dean Stanton!) and Carroll O’Conner’s pompous twit of a general. In 3K, Clooney and Spike Jonze are great, plus some of the supporting players, such as the guy playing the US-educated Iraqi, who delivers a great speech explaining just why he is going to torture one of the Americans.
On the downside, KH certainly shows its age a bit (that ridiculous theme by the Mike Curb Congregation really gets up my snout), and as a previous poster mentioned, one gets the impression that a few essential scenes were left out to keep the running time down. As far as 3K goes, the visual tricks are overdone and the ending is a bit of a mess, IMO.
One thing I find interesting is that despite the obvious similarities in tone and subject, KH has never been highly thought of by critics, while 3K was generally got raves on its release. Resentment of KH seems to have been based on its irreverence twards American participation in WWII, and a certain lack of political correctness at a time when American involement in Vietnam was at its height. Nevertheless, I can’t agree that KH was intended only as a straight comedy; there are certainly political aspects to the story, although they are not expressed as overtly as in 3K.
If you put a gun to my head, I suppose I would go with KH, for being the first, and perhaps for having a screenplay that is a little more subtle about its themes.
Other fave war movies? 12 O’Clock High, Apocalypse Now, Bridge on the River Kwai, Cross of Iron, Catch-22, Das Boot, The Deer Hunter, Full Metal Jacket, MAS*H, Paths of Glory, Stalag 17, and The Train, in no particular order. I’ll probably think of more later.