Broken Base: The remake is roundly bashed for not being theexact same game as the original, while by itself not being half-bad game. On the other hand, hatedom is perfectly right when pointing out it does cut away about 2/3 of original game content and it goes without mentioning the extremely mishandled production (missing the anniversary by a year). A decade after premiere the fandom is still divided over the game.
Foe Yay: Is really played up between Lara and Larson, especially when compared to the original.
It's Easy, So It Sucks: Original game was firmly in Nintendo Hard territory. Anniversary, with checkpoints every five seconds, regeneration of health upon deathnote which probably earned the most flak, streamlined to bare basics level design and ability to perform One Hit Kills is a far cry of that, earning a lot of snark remarks from fandom.
Misaimed Marketing: Ho boy... The game was made for the 10th anniversary of the entire frachise. The fact it was released almost a whole year too late is just the start of the problems with marketing and mishandling of entire production and its promotion. The game by default was created to capitalise on the anniversary, nostalgia factor, bring new players to the franchise and familiarise Crystal Dynamics fledging fandom with the roots of the series. The marketing in the same time was aiming fully into players completely new to the entire franchise, ignoring all the nostalgia-related factors and pre-existing fandom, which by default was making most of potential players and buyers. Then the marketing department decided to make a production decisions, reducing a lot of levels to their most iconic elements and nothing else. The final effect was a campaign not even trying to appeal to pre-existing fandom, marketing openly ignoring the fact it was made as a remake of one of the most legendary games ever made and never actually catching attention of non-fans due to relatively small campaign (especially when compared with Legend's massive marketing). The game is the lowest selling title in the entire franchise so far.
The musical cues when fighting enemies. The music itself isn't bad or anything (though it can get manic, repetitive, and very over-the-top). The main issue is the fact that - at least after a certain point very early on in the game - virtually every single enemy encounter is scored by the music blasting and blasting until the fight's over, and it happens constantly - especially in Atlantis. It can really ruin the tension of enemy encounters, and not knowing whether or not you're still in danger, and can ruin the quiet atmosphere as well. Even the rats get their own score for when you encounter them.
Nightmare Fuel: Anything involving the Atlanteans, but especially the sacks from which they burst when you come too close.
There's also Lara's various deaths via Quick Time Events. While they are normally censored, she still dies in pretty gruesome ways, even compared to earlier games.
So Okay, It's Average: When taken outside the context of controversy surronding the sole idea of remaking original Tomb Raider and the nasty bits about Core Design getting the short end of the stick, the game is just... average. It makes many things much more spectacular, while other are simply uninspired and bland, but in the end of the day Anniversary neither outright bad, nor special in any way. In fact, it's probably the most average Tomb Raider in existence.
That One Boss: Third ledge above the lava, "Great Pyramid", Anniversary.
They Changed It, Now It Sucks: While some of the fandom still wasn't entirely hot on this new Lara, any Video Game Remake inevitably risks falling prey to this trope. Specifically, some people were not happy with the way some levels were streamlined, with much of the siderooms being removed or reappearing elsewhere in the game. Lara's motivations were also called in question, as she no longer appears to raid tombs "for sport", but to find out what happened to her mother. Some fans of the original Tomb Raider screamed in fury at the T.rex encounter being a boss battle largely played by quick-time events.
This is quite possibly the least faithful Video Game Remake of all time. It resembles a Hollywood-style movie remake, in that all of the game's content has been rebuilt and re-imagined from the ground up. The changes are insurmountable and the game is only faithful to the original Tomb Raider in Broad Strokes.
Tough Act to Follow: Due to the absolutely legendary status of the original game, it was inevitable. And since Crystal Dynamics took a lot of liberties upon making Anniversary in both gameplay and plot department, the older part of the fandom virtually disinherited the game.