The reason for the remake, is that Charles Portis original book was about a young lady (Mattie Ross) and her experience in tracking down her father's murder and it was set in western Arkansas and eastern Oklahoma.
The screenwriter who did the original adaptation rewrote the story as a vehicle for John Wayne to be the star and set itup to film in Narrow Gauge (RGS) country.
The Coen brothers wanted to do the remake to follow the book, and be a story about Mattie Ross, not about Rooster Cogburn. Incidentally, Jeff Bridges who plays Rooster, is exactly the same age as Wayne when he shot the movie.