The TLDR for Sony is that Concord basically gave them PTSD and made them VERY skittish and between the time needed for Kojima's games, the price tag and the fact that they would not be console exclusive, they decided they wanted to pull out. 

The TLDR for Xbox is that they want an "in" into Asia which they belive Kojima can help them with, also in addition to games, want to branch off into other forms of media and and with Kojima being basically a movie director in addition to a game one, and working with various celebrities and other directors (such as Jordan Peel with OD), they believe he and Kojima Productions can ALSO help with this.

Another reason is that, with Kojima products being multiplat (though in this case I mean PS and PC), Sony doesn't benefit monetarily from any revenue made from Kojima's products on PC (they would only produce on PS), meanwhile, with Microsoft's long and stories history of supporting PC in addition to Xbox, they would produce the game on both Xbox AND PC and would thus then benefit monetarily from both.

And finally, though Schreier didn't mention/talk about this, to put my own "two cents" on this, Xbox, and Microsoft over them, still possess "big dick, fuck you" money, which Sony...does not, and whilst Microsoft has shown they want to tighten the leash a bit on such expenditures that use that money, that doesn't mean they've completely ruled out spending it, just that they want to be more judicious in who gets that type of funding. For the reasons listed above, they believe that Kojima is worth that investment and footing such a price tag is less strenuous on them then it would be to Sony, who are trying to work in MUCH tighter margins, as exemplified by their closure of Destiny and their move away from physical games, Sony has decided to very much move in the direction of "penny pinching". 

A deep dive on the whole situation between Sony, Kojima and Microsoft (Xbox)