The tones are completely different. Hell or High Water is a laid-back modern western about small town economic woes plus a subplot with one racially-charged buddy cop duo.
Nocturnal Animals is a dark and mysterious neo-noir with a movie within a movie and a murder subplot.
Cinematography is different, the use of color is different, the cast is different, the genre is different, the themes are different, the only thing they have in common is a cop with a cowboy hat and a few scenes that take place in the southwest.
I'm only harping on this cause it seems to be a common thing online where people make these dubious comparisons all the time. Like calling Nolan's films Kubrickian. Their films are nothing alike.