The reason that the original True Grit might not have appealed to many JW fans is that he played some of the movie as satire: a dissolute, n'er do well, drunken, over the hill man who had a fast and loose relationship with the law he was sworn to enforce, played with comedic overtones. Then, in the latter part of the movie, he morphed into the character we all love: the strong, brave, and stalwart man who braves any odds to do what is right, and who IS right in what he does.
Personally, I think True Grit was one of his best westerns, if you look at the man he played. In finding himself and saving the girl, he actually came to love her, and looked after her like the father she lost. It's very similar to The Searchers, in terms of the character, except that Ethan Edwards was not a parody at any time; he was twisted by hate and lost love. At the end of the movie, Edwards did find his humanity, just as Cogburn found his way back to decency.