I played all three of these in a row and I'm now officially burned out on The New Adventures of Lara Croft. But they were fun! Well, at least the first and second one were.
I never cared about the original Tomb Raider (1996) game(s). I remember liking the movies, I even liked the sequel Lara Croft - Tomb Raider: The Cradle of Life (2003); you know a movie is good when it has both a hyphen and a colon. So I didn't expect a whole lot from the reboot when I picked it up on super discount almost 10 years later, but I was pleasantly surprised by Tomb Raider (2013). It's true, however, that there ain't too much actual Tomb Raidin' in it. You do a lot of arrow shootin', a lot of bullet shootin', a lot of fightin'. It was way more combat heavy than I expected, which I definitely appreciated. "Tombs," such as they are (most of them are actually just caves somewhere in the woods), mainly exist off the beaten path of your mission and consist of a fairly simple, physics-based puzzle. They serve the purpose, however, of providing you with skill points on completion to upgrade Lara's weapons, equipment, and self. Of the three "survivor" games, Tomb Raider is by far the simplest, and I think that's what I liked about it the most: it's just a fun action game.
Rise of the Tomb Raider (2015) is the refined version of Tomb Raider. Everything is better. It's gorgeous, the animation in particular is excellent, the combat and exploration has opened up considerably, the spectacle is larger, the storytelling is pretty decent, and there's even more tombs! A lot more tombs. There's a lot more of everything. I think it becomes too much of a collect-a-thon, there's too many things to collect and craft and keep track of. There's a simplicity to the first game that I still prefer, but it's impossible to deny how incredible Rise truly is. Even if you, like me, don't have any particular attachment to the character or franchise and you don't mind if Lara Croft is less Tomb Raider and more Murder Badass Gal, Rise remains an excellent, all-purpose, generally excellent third-person action game.
I don't totally know what happened with Shadow of the Tomb Raider (2018). I really grew to hate this one. Technically, it's up there with Rise, maybe in some ways surpassing it: the traversal has never been better, the world is gorgeous, even if the character models look a bit off. The big problem, however, is how off-balance it feels in structure; by that I mean the balance between narrative, exploration, and combat. The writing is already awful, just belabored and breathless and half-hearted, and on top of that it has one of the biggest narrative drop-offs in gaming history. Shadow goes to hell as soon as you take Lara to Paititi (roughly midway through the game or so) and it never recovers. I almost gave up on it because you get sent on a thousand uninteresting fetch quests that don't even have action in them in a game that already struggles with having enough action in it. When the action picks up the game is fun, but there's an entire skill tree that ultimately doesn't matter because not enough happens and none of the skills have anything to do with all the talking in it. I don't think there's ever been a prettier failure than Shadow.