It has been recently confirmed from an official statement that Battlefield 4 multiplayer save states for current gen consoles can be transferred to next-gen consoles.
via N4G: pc news feed http://n4g.com/news/1363474/battlefield-4-will-allow-for-multiplayer-save-transfers-from-current-to-next-gen-consoles
via N4G: pc news feed http://n4g.com/news/1363474/battlefield-4-will-allow-for-multiplayer-save-transfers-from-current-to-next-gen-consoles