In the latest issue of The Official Xbox Magazine, campaign director Jason Blundell explained why the last generation versions of Call of Duty: Black Ops III does not have the campaign. The main reason is the lack of memory on the PlayStation 3 and Xbox 360, but the full quote below better explains it.

Let’s imagine I have my customised weapon and I’ve made it with a stock and all this extended mag and so forth. For you as a co-op player to see what weapon I have, you have to have loaded in the memory – in resident memory – every single weapon customisation. Current-gen memory just can’t do that. You’d have to have everything loaded otherwise you just can’t see what I’m carrying. You know you could simplify things down, but I think [Activision] made the right choice because I would hate for people to get an experience that wasn’t true to the vision of it.