No. Multiplayer progression—rank, unlocks, stats, battlepacks—cannot be transferred from Xbox 360 to Xbox One for Battlefield 4. Data is stored separately per platform with no cross-gen linking system.
Starting fresh on Xbox One means experiencing Battlefield 4 at its best: 64-player Conquest on maps like Golmud Railway and Siege of Shanghai, 60fps gunplay, and the full "Levolution" destruction. View it as a chance to re-climb the ranks with better hardware!