Full exclusivity no longer make sense for 3rd party developers. Porting is much easier and less expensive than before, and you have two platforms that are around as massive or bigger than Playsation. Timed exclusivity on the other hand does make a lot of sense. Full exclusivity for a platform holder, which only Nintendo does these days, is also logical.
The difference between Playstation and Xbox is that one is slowly and only partly losing its identity (and bolstering PC), and the other already did many years ago. The real winner here is Valve.
Microsoft can easily make Xbox very relevant again, but it would come at the great price of damaging their IP's including CoD. MS is only the biggest publisher out there because they're a multi platform company. If they return to full Xbox exclusivity, Nintendo would probably beat them, and Sony too might.