You can use the same account on both platforms, just log in and everything is there. Only thing you have to do yourself is setup hotbars but it may be possible to use the launcher to save the settings on your first gamesystem and then restore it on the other one, not shure.

Second part, you do need to buy the game on both systems. You do not need to buy the collectors editions for both, only buy one collectors edition and for the other gamesystem buy just the base game/expansion.