No Country for Old Men was a prestigious Oscar pic from the get-go, released at the height of Oscar season, directed by two icons of cinema, The Coen Brothers, and featured one of the most memorable characters of the past decade in Anton Chigurh.
Hell or High Water released in August - usually a dumping ground for studios - from a director with only one other semi-notable credit (Starred Up), and from the trailers, honestly kind of sort of looked like a bargain bin western. "Fluke" is the wrong word, but the fact that it ended up being as great as it was, and met the acclaim it did, was not expected in the least. Even with all the praise and Oscar nominations since then, it's surprising to me that anyone would expect NCFOM-level greatness. I obviously loved HOHW, but the pedigree for that kind of expectation just isn't there.
I'm likely over-analyzing it, and it's probably as simple as two, critically acclaimed, Texas-set westerns being measured against each other, but I would have thought that it would be fairy easy to distinguish the difference in reception and pop culture impact. Not to jump all over you for not loving it or anything, it's just genuinely interesting to me how/why people compare/contrast the movies they do, and the standards they hold them to.