First, there's the whole thing (that I mentioned somewhere, I think on Facebook) that the original is the only John Wayne movie my father ever liked. Now, that's a lot of movies to rule out. (He had a lot of prejudices against stars and directors, see below.) He loved westerns in the abstract, but it was hard to find any specific ones he liked, because his criteria were so many and so strict:
No happy endings.
The protagonist should preferably die at the end, but whether he does or not, whatever he accomplished can't be redemptive, or even particularly helpful. If it benefits the townspeople at all, they should be amply shown (in my father's interpretation, at least) to be so uncaring, ungrateful, or unaware of the protagonist's deeds that it can still be read as completely futile.
No cute kids.
The protagonist can't be a nice guy, and esp. NO JIMMY STEWART! EVER! (some of these rules transcend genre)
Violence = there could be some, but it had to be pretty subdued. He was quite a prude when it came to violence and found Peckinpah and Eastwood appalling.
The protagonist has to sleep with lots of women. Basically however many are in the cast of an appropriate age, preferably. Any hint that the protagonist is chaste or might have some scruples takes us back to "no nice guys" rule above. (Deep down, it was the only disagreement we ever had over The Prisoner TV series - #6 didn't get enough ass, and that diminished him so thoroughly in my father's esteem that he could never take him as heroic or admirable.)
Should be "closing of the West" setting, though not with any nostaligia, nor with any preference for what came after - just more of a fatalistic acceptance that "That's the way it is, chum: no more buffalo, no more Indians, no more gunfights - no more YOU. If you want to kill some people while you shuffle off to die, that's fine." (Sheesh, these are depressing when I actually write them down)
Now, as you might imagine, with those rules, there isn't much left. I'd say if strictly applied, we'd be down to
Treasure of the Sierra Madre
Butch Cassidy and the Sundance Kid
Lonely Are the Brave (no one's ever heard of it - but I do highly recommend it though it is unrelentingly grim)
And then, breaking several of the rules (as well as having Wayne in it) - True Grit.
Well, I guess we'll never know the answer to why he made an exception for that one. (Sorry, didn't mean to lead up to some big epiphany - it really is just a cool conundrum, I think.)
Now, the new one. I have to say, the girl's character was wanting. Not in acting, surely - the whole thing was well acted, and with the Coen Bros usual skill at presenting enormous, breathtaking vistas in the background, paired against up-close, dirty, spitty scenes of violence (there's a lot of spit in one scene, and it's not even a violent one). The scene in the cabin - you're pretty sure it'll end badly, but what happens is just so... so... filthy. But we know so much about the two male leads, and I have no idea why the girl knows law codes, why she's so fiercely determined to avenge her father (knowing nothing much of their relationship at all, except they went coon hunting once), or why she then lives her life unmarried and fairly dyspeptic toward the whole human race. Imagine Saving Private Ryan if, after they save Ryan, he goes home and is pretty much a misanthrope and loner, and then thinks back to whether the other men's sacrifice was worth it. (And yes, I find the ending of that movie too rosy by half, so I'm using it as an example at the other extreme, not a model.) So I did feel a bit let down at the end.
Oh, and why did everyone over-enunciate everything? Not just the elevated diction, that was also distracting, but saying every word clearly and with no contractions: "I did not. Know. That. Man." Sounded really weird and took me out of the experience throughout.