The Xbox One's Jamais Vu mission stars Raiden, who runs a lot faster than Snake, but otherwise operates the same. Your goal in this mission is to eliminate a gang of body snatchers who can only be detected by tagging them with your binoculars. It's a fun little jaunt and it gives non-lethal-focused players like yours truly a chance to muck about with the game's deadlier weaponry, but it's ultimately insubstantial and ends with a frustrating, overly long shooting sequence.
The PS4's Deja Vu mission is the real surprise. In this goofy side-quest you're tasked with recreating photographs of areas in the level that recall the first Metal Gear Solid. Find the right angle to snap a pic of a chopper and two soldiers and the picture is automatically taken, which brings with it a funny cutscene comparing the new game to its 1998 forbear. Like Jamais Vu, it's not a huge boon, but it is an amusing aside for exploration-loving, secret-hunting players like myself.
Unfortunately both console-exclusive missions take a lot of doing to unlock. Konami won't let me say how you unlock them, but let's just say that it's something that would have taken me a very long time to do without outside help. Being the stubborn player that I am, I actually never unlocked them on my file and simply switched demo stations to scope them out.