Right from the outset the most obvious change, aside from the obligatory visual improvements the Legend engine brings to things, comes in the way Lara feels to control. Lara seems to instinctively know what you're trying to get her to do, always doing her best to hit the marks you're aiming for, helpfully grabbing onto any ledges you've just missed with the tips of her fingers. That's not to say the game is now boringly easy, simply that its less frustrating and when you fail it's because you messed up, not because the game is being unfairly fussy about things.
Ultimately there's very little to moan about here aside from the still weak combat, it may not be cutting edge (to be fair, it was never meant to be) but it's far more enjoyable than a lot of other completely new games out there. The fact that everything, from the level design to the gameplay concept, in Anniversary is now over a decade old and yet remains so captivating speaks volumes about the almost flawless design of the original.