Have indeed played this as well. It's a good third person game. Feels a bit more like Far Cry in the fact that you do a lot of climbing, collecting, hunting and... well... raiding tombs
There are animals to kill and scrap to collect. You upgrade weapons and gear with the stuff etc. You unlock skills as you level up. All the typical things you come to expect.
Has a decent story and good voice acting. Character graphics and environments are really, really good.
Levels are large but somewhat linear. Not an open world game at all, but the levels are pretty darn big. You are dropped into a location and have to scout it out to find all the goodies, secret entrances to side areas and so forth. AI is competent, but not great. Basically a large stealth game of picking them off one by one as you move through an area. There are some really huge areas that have a lot of baddies to mix up the levels (sometimes it's a big firefight or a lot of melee enemies swarm you) and some of the tombs are really cool to explore.
I don't have any real big hates on this one. It's a solid game that does what it intends to do. If you've ever played any of the other Tomb Raider games you can see that it sticks to those roots in it's general look and play. Some of the climbing puzzles and the timing were a little frustrating for me to figure out. I've never been super good at QTE with my slow reflexes. Eventually I figured them out, but I almost gave up once or twice because of the frustration and lack of clear guidance about what I was supposed to do. I guess for me the action puzzles were the only thing that REALLY annoyed me.
Also there's no first person, but the way the bow draws in a kind of "fake third person" as your character sort of moves to the side and you are focusing on the center of the screen... hard to explain, but it fires sort of like first person, but in a third person view. If that makes sense.
It's a solid AAA game. I like it. I like the Far Cry games better though