Navi was on roadmaps before the PS4 was out, Sony has nothing to do with it or it's developments. They just choose the chip early for their Next Gen console, that's it.
Microsoft will most likely choose the same one, there's not much other choice, either. NVidia would get too expensive and would mean 2 chips, not an APU.
The Nintendo eShop rating Thread: http://gamrconnect.vgchartz.com/thread.php?id=237454