Just finished the new Tomb Raider game and I'd have to give it extremely high marks. I actually enjoyed it quite a bit more than Bioshock: Infinite, though for graphics and creativity, Bioshock was probably the better game.
I've played every single Tomb Raider game since the original came out in 1996, and finished all but one (the practically unplayable "Angel of Darkness" which essentially killed the original series). I think I'd rank Tomb Raider (2013) as the #2 best Tomb Raider, not quite as engaging as Tomb Raider: Anniversary and perhaps slightly better than Tomb Raider: Last Revelation, though not nearly as long and challenging.
Essentially, you've got your second reboot of the series. The original series was puzzle oriented, with combat largely a way of breaking up the frustrating grind of trying to figure out how in the hell you were supposed to get out of each tomb. The second set of games were launched in 2006, largely a graphically enhanced version of Tomb Raider, more combat intensive to attract the FPS crowd but still essentially adventure games with challenging puzzles that kept you thinking more than shooting.
Tomb Raider (2013) is more of a storyline adventure. There's significantly more combat and significantly fewer tombs, but clever use of navigation tools like rope arrows, climbable and breakable walls, zip lines and quick travel really immerse you in the adventure. You're stranded on an island, there are lots of people trying to kill your archaeological team and each level is a portion of the island with its own unique challenges (such as finding several birds' nests to complete the "egg poacher" challenge).
The game charts your progress, not just toward the finale, but also according to how many of the challenges you complete and you can quick travel back to earlier levels to search for hidden things you might have missed. Initially I spent very little time focusing on the challenges but as the game progressed and I became more adept at recognizing areas I could access off the main path, I found myself searching for challenge achievements as well as pushing the story forward. Before I entered the final few levels, I went back and cleaned up all of the stuff I had missed, which was a lot of fun and allowed me to finish the game with 100% rating.
Unlike earlier versions of the game, the heroine Lara Croft "levels" as she kills enemies, loots prey and completes challenges. Levels allow you to select certain perks which make her more adept at fighting and hunting. Additionally, looting salvage from enemies and crates allows you to upgrade your weapons, making you a more capable killer as the game progresses. I'm not sure that I've ever killed the final boss in a game without a single death, but I manage the feat in Tomb Raider (2013) so perhaps the combat was too easy, or perhaps my dedication to completing all of the challenges simply made Lara and her weapons more powerful than they really needed to be. Most of my deaths came from falling, which is typical of any Tomb Raider game.
Overall, I'd definitely recommend this title. If you've been reading up on the new games and saw that both Tomb Raider and Bioshock: Infinite have been getting stellar reviews, I'd recommend Tomb Raider over Bioshock. Perhaps it was just my familiarity with the series, but I definitely had more fun with Tomb Raider. Now all we need is a few more tombs in the next game.