So think about which version you want before you buy.
If you buy and play Call of Duty: Black Ops 3 on the Xbox 360 or PlayStation 3, beware! Your multiplayer mode stats will not transfer over to the Xbox One or PlayStation 4, even if you purchase the game for a system in the same family. So basically, unless you don’t really care about the multiplayer mode at all, think twice before you splurge on a previous generation version of Black Ops 3, and ask yourself if it might not be better to wait till you can buy the game for one of the new consoles.
The previous two Call of Duty games released for the current crop of consoles – Ghosts and Advanced Warfare – did allow for a one time transition of multiplayer stats from Xbox 360 to Xbox One, or PS3 to PS4. That said, the same developer was behind all versions of those games, as opposed to Black Ops 3, where Treyarch is only handling the PS4 and Xbox One versions, so maybe that is the reason for this break in practice.
Whatever it is, it is clear now that Activision is trying to transition the entire Call of Duty base on to the current generation.
Call of Duty: Black Ops 3 launches November 6 for PS3, PS4, Xbox 360, Xbox One, and PC.