One factor in the AMD vs. nVidia is that supplying hardware for consoles is in itself not a very profitable undertaking. AMD wont be making any significant amount of profit of the console hardware sales.
One of the big reasons why nVidia is not supplying any of the console hardware solutions is that nVidia is at a point where they can sell all the cards that their factories can produce. Since nVidia makes a bigger profit selling the cards to laptops, mobile instruments or PC Gamers than they would have if they sold the same chip card to MS or Sony instead.
AMD was in the opposite situation when deals were made for this generation of console hardware. AMD build a couple of new major factories in Germany and Texas in the last decade, with the slowing of the world economy AMD was struggling to pay the bills and struggling to find enough business to keep their factories busy. So for AMD the console deals were a life saver. They might not make much at all per conole, but they do cover their costs which help pay the bills for their factories. It could also give them a powerful edge in the overall gaming market through the next gen. With both XBone and PS4 using AMD it might quickly become the standard that games are build to support.