Hmmm... you need a third box in that survey, methinks. I like both films because they attack their subject matter in different ways and both have great and not so great points. SPR was/is Speilberg's tribute to the D-Day veterans and works on that more visceral level you didn't see in something like The Longest Day or other old war films. Sure, some of the film doesn't hold up to scrutiny, but what's there is shot and edited brilliantly. I'm an American, but I found it a bit to ham-heavy on the patriotism, although that's what it was going for.
Malick's film is a more languidly paced look at men in the Pacific Theater that's not going to get some war movie fans excited if they go in expecting gung-heroic action and everyone gritting their teeth while blasting "Japs out of the trees" (as I overheard one veteran say to the person who took him to the screening I went to). He actually liked the film, by the way because he'd served in the Pacific and noted things the director got right and wrong. The one thing that stuck with me was him nothing "They never get the sense of smell right in these movies. You can never get that stench of death out of your mind even when you get used to it." That blew my mind, but I loved the visual power of the film from beginning to end.
In short, I can't decide which is "better" because both are good at what they attempted.
Without a doubt has to be The Thin Red Line for me!
Saving Private Ryan may have the great opening scene but in my view is very weak in terms of story and a very forgettable film, I do regard it as very overrated.
Where as I regard The Thin Red Line as a masterpiece, it is beautifully crafted, emotionally involving and a poetic film on so many levels. I can appreciate it may not be to everyone's taste, but I regard it as Malick's best film and one of my all time favourites.
I'm a Spielberg fan!