PowerVR if you're not familiar with them are the GPUs for the recent iPhone/iPads. They generally specialize (as you would expect) in low power consumption mobile processors. 

A few months ago they unveiled the PowerVR GT7900, an extremely powerful and cheap processor that sucks just a bit too much juice for a handheld but would be suitable for a micro-console:

http://liliputing.com/2015/02/imagination-unveils-powervr-gt7900-graphics-for-low-cost-game-consoles.html

The thing is pretty beastly in performance too, pumps out 800 GFLOPS in FP32 mode and 1.6 TFLOPS in FP16 mode. That's even better than the Tegra X1. 

This would be a fairly large upgrade on the Wii U. 

It's low cost (cheap). 

It can scale very easily down to a mobile device too (Portable NX meet Home NX) as it is basically just a souped up mobile processor to begin with. 

Being that it's a mobile part, it likely consumes far less electricity than even the Wii U, and can be put into a form factor that's even smaller. So that would be a plus-plus for Nintendo.

I wouldn't count out AMD from getting the gig, but I have to wonder if Nintendo would look very carefully at PowerVR too. First products using this processor will go on sale later this year, so it would be ready for a fall 2016 launch if that's what Nintendo wanted to do as well. 

The whole notion that an NX handheld and console would have the same power needs to die already.

They wouldn't, this chip runs too hot/powerful to run in a portable config I think, but it would be fine in a microconsole form. PowerVR is specifically tagetting it for home use. 

The handheld version would have to be like half the power but it would be very easy to scale graphics up and down. 

Even at half, 400 GFLOPS in a handheld would be pretty freaking awesome.