Via the official release on the Call of Duty website, Activision has revealed the details for last generation versions of the game. They note that the game was fully built with PS4, Xbox One, and PC in mind and that some details needed to be scaled back for PS3 and Xbox 360 users.
They then explain that they made the decision to fully cut the campaign from the game for those users. They note the 4 player experience and mechanics for the game simply cannot be translated well to older consoles.
The Black Ops 3 PS3 and Xbox 360 versions will feature Multiplayer and Zombies gameplay only, not Campaign. The ambitious scope of the 1-4 player coop Campaign design of the PS4, Xbox One and PC versions could not be faithfully recreated on old generation hardware.
The good news is that zombies and the online multiplayer are fully intact, which is where most COD users float to anyway. The slightly stripped down version of the game will retail for $49.99 for old gen users, but it also includes a download copy of the original Black Ops.