I'm a big John Wayne fan, and a fan of his True Grit, (also a longtime fan of the book) but I saw the new one, and then watched the old one on DVD about a week later, and except for a few scenes where Wayne was at his best, the new version, for me, was much better than the 1969 version.
Hailee Steinfeld as Mattie Ross, was just utterly amazing, far and away better than Kim Darby. She came across much more like the girl in the book, very determined and angry, whereas Darby came across as petulant and whiny.
Matt Damon, is the weakest link in the cast, but at least he did a fair job of playing the Ranger as he was intended, to be a bit of a moronic poof. But even he was better than Glenn Campbell, which was possibly the worst case of miscasting in Hollywood history.
Jeff Bridges as Rooster, borders on cinematic perfection. As much as I like John Wayne, he had a bad habit of "cleaning up" characters he played, and often went to far. While the first film mentioned his past with Quantrell and Bloody Bill, they greatly downplayed it from the book. I really liked how the new version showed a much more flawed and violent Rooster Cogburn.