Okay so there's a few rumors going around, mostly from Eurogamer / DigitalFoundry, that claim the Nintendo NX is going to be powered by an NVIDIA Tegra system on a chip (SoC). DigitalFoundry, specifically, cites multiple sources who claim that their Nintendo NX development kits integrate the Tegra X1 design, as seen in the Google Pixel C. That said, the Nintendo NX release date, March 2017, does provide enough time for them to switch to NVIDIA's upcoming Pascal Tegra design, rumored to be called the Tegra X2, which uses NVIDIA's custom-designed Denver CPU cores.
Preamble aside, here's what I think about the whole situation.
First, the Tegra X1 would be quite a small jump in performance over the WiiU. The WiiU's GPU, “Latte”, has 320 shaders clocked at 550 MHz, and it was based on AMD's TeraScale 1 architecture. Because these stream processors have single-cycle multiply-add for floating point values, you can get its FLOP rating by multiplying 320 shaders, 550,000,000 cycles per second, and 2 operations per clock (one multiply and one add). This yields 352 GFLOPs. The Tegra X1 is rated at 512 GFLOPs, which is just 45% more than the previous generation.
This is a very tiny jump, unless they indeed use Pascal-based graphics. If this is the case, you will likely see a launch selection of games ported from WiiU and a few games that use whatever new feature Nintendo has. One rumor is that the console will be kind-of like the WiiU controller, with detachable controllers. If this is true, it's a bit unclear how this will affect games in a revolutionary way, but we might be missing a key bit of info that ties it all together.
As for the choice of ARM over x86… well. First, this obviously allows Nintendo to choose from a wider selection of manufacturers than AMD, Intel, and VIA, and certainly more than IBM with their previous, Power-based chips. That said, it also jives with Nintendo's interest in the mobile market. They joined The Khronos Group and I'm pretty sure they've said they are interested in Vulkan, which is becoming the high-end graphics API for Android, supported by Google and others. That said, I'm not sure how many engineers exist that specialize in ARM optimization, as most mobile platforms try to abstract this as much as possible, but this could be Nintendo's attempt to settle on a standardized instruction set, and they opted for mobile over PC (versus Sony and especially Microsoft, who want consoles to follow high-end gaming on the desktop).
Why? Well that would just be speculating on speculation about speculation. I'll stop here.