Well, I've seen both films several times and read the book, so here goes.
For me, westerns are like sci-fi films, they say more about the period in which they were made rather than the period that they are depicting. This is definitely 'grittier' than the John Wayne, but that alone does not make it a better film, just a different one. Jeff Bridges is excellent, althogh it is true his accent is very difficult to understand some of the time, but perseverence brings rewards. Matt Damon is ok, Hailleee Steinfeld is very good (and should have been nominated for actress, not supporting actress, as she is clearly the lead charecter in this version, as well as the book).
As to it being more faithful to the book than the previous version, this is not true. It has the book's ending, which the John Wayne film does not, but there are truncated scenes, and missing ones (the part in the book where the deal is made at the start, for instance, is mostly missing), and some other scenes are altered (such as LeBoeuf going off before Maddy meets Chaney, which the John Wayne version has the same as the book). In all, however, it is a very good film, and so is the John Wayne one, neither are rubbish and it is churlish of anyone to say so.
The book is outstanding, however, and I would recommend it to anyone.