An option added to bungie.net to transfer vault items back and forth between the PS4 and Xbox One. If a player has two linked accounts it should be possible on Bungie's side of things to move inventory around on their servers. One console would not directly interact with its rival console's network so cross network play is would not be necessary. I made a permanent switch to Xbox One from the PS4 and all of my weapons and gear from my PS4 days are sitting in the vault unused.