I did not like the previous Tomb Raider games, but decided to give this one a chance. I'm glad I did.
The opening cut scenes immediately impressed me. The first levels that followed were a bit disappointing, not least of which because of the excessive use of quick time events and how closed the flow of action was--often one step away from a railroad game. Fortunately, this quickly started changing and while not as open world as Far Cry 3, it was better than most.
About halfway through, you get enough weapons and varied enemies that the game really takes off, the action and fun only being marred by some truly awful, and sometimes baffling, quick time event moments. Fortunately, the fun factor outweighs those moments to a significant degree.
One thing I really enjoyed is that many of the puzzles were real puzzles and both fun and satisfying to solve. It's been a long time since I played a game like that.
On top of all of this, the cut scenes are among the best I've ever scene and the story is one of the best I've seen in a computer game. The rendering of Laura and other characters, and the voice acting are superb.
I highly recommend this game.