I saw both True Grits the other day - first the 1969 version with John Wayne and then the new Coen brothers version - within a couple of hours of each other.
A frequent comment I've heard about the versions is that the Coen brothers version is much closer to the book. I'm not sure about that - I haven't read the book. But I will say that the two movies are actually very similar to each other as far as telling the story - and many of the 2010 shots were very similar to the 1969 shots.
The beginning and the end are the most different for each movie - there are scenes of the murdered father in the earlier version. The outcomes for the characters are a bit different, especially the LeBoeuf character - and let me state for the record that Matt Damon looks very fine indeed in that role - much sexier than Glenn Campbell in the '69 version.
At least this review admits that "the screenplays are eerily close."
Fun fact - the '69 version had Dennis Hopper and Robert Duvall as outlaws. And Dennis Hopper got his fingers chopped off. I was surprised that the Coen brother's filming of the finger-chopping bit was only a little more graphic than the '69 version.
The '69 version did leave out the guy with the bear skin - although since the encounter with him furthers the plot not at all, as amusingly weird as it is - that was probably the better choice anyway.
And I also have to say that the first version had a stronger emotional impact for me at the end - even if it was a tad cheezy - than the Coen brothers version - but I think that's because the Coens try so hard (or maybe it comes naturally to them) to keep emotional distance from humans. And so for me the most emotional moment in the 2010 True Grit was over Mattie's horse. I cried for the horse. You'll understand if you see the movie.