Sonic Adventure DX: Director's Cut, although it has the same name as the GameCube and PC expanded version of the original Dreamcast game, is actually a bundle with both the game released first for Xbox 360 and PlayStation 3 under the title of "Sonic Adventure" and its DLC, "Sonic Adventure DX Upgrade". These two games are enhanced ports of the PC version of the original "Sonic Adventure DX: Director's Cut". This bundle/enhanced port adds full widescreen support for the game.
