I've seen and enjoyed both versions and there's no doubt (for me) which comes out on top - the new one. Jeff Bridges' acting isn't OTT, it's just that he has so much more in his artistic repertoire than John Wayne did. I also didn't see Hailee Steinfeld as a one note performance. If anything, I found her much more believable as a late nineteenth century adolescent female than Kim Darby. As for her braids, if there were any scenes showing her in bed with her hair in braids they haven't registered with me. Perhaps when they are all out on the trail it was less believable that she would keep her hair perfectly braided, but the point is not important enough to detract from her performance.

I haven't read the book, so can't comment on how faithful either film is to what Charles Portis wrote.