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.
After a report on Kotaku revealed that player progression for single player games making the transition from current to next gen may be lost, an EA spokesperson confirmed the following:
Yes, at launch of the next-gen consoles, you will be able to bring your multiplayer progress from current-gen to next-gen with you – your rank, score, K/D ratio, wins, time played and more. The stats transfer works from PS3 to PS4 and Xbox 360 to Xbox One.
It’s good to know that if you choose to purchase the PS3 or Xbox 360 version of Battlefield 4, you can safely transfer over all your hard work in the multiplayer.