I have not bought Halo Anniversary but I will. Yes, it is the exact same game except it is now rendered in HD (16x9) for the 360. Also, they reskinned everything in Halo Reach graphics and models and you can switch between the old graphics and the Reach graphics. They re-recorded the sound effects and game music, added skulls for replayability, and included some Halo CE maps that you can play in the Halo Reach multiplayer. If you haven't played Halo CE I highly recommend this game. It is a classic and is the reason the FPS platform exploded on console systems.