Same with PS3 to PS4
A lot of people have grown increasingly resilient to upgrading to the current generation for fear of losing their data. With some games a painless transfer process is an option though, and one of those titles will be Minecraft.
Although PS3 and PS4 transfer capabilities were already confirmed (Vita is still up in the air), Microsoft's Phil Spencer has also noted that the same thing will be possible when moving from the 360 to the Xbox One.
There's still no news on Cross-Buy or discount options though.
Phil Spencer [Twitter]