An AMD x86 CPU would be far more power hungry than an ARM processor. That said, AMD are in a position (or will be in about 2 years time when they round up development on their ARM chips) where they can actually supply an ARM and an x86 SOC to Nintendo (with the same GPU architecture on both chips).

This would fit quite favourably with the NX concept. And whilst x86 CPUs can emulate ARM processors, I'm not sure Nintendo would favor this as it's fairly inefficient. I think they'll probably look to make dev tools that can translate the same set of code for both architectures. I think Sony do something similar with PS4 and Vita.

I have a hard time believing that considering the game wasnt specifically developed for the ps4. how do we know framedrops are due to the ps4 not being powerful enough and not because the developers didnt do a good enough job preventing frame drops?

Another option is to put an ARM CPU and an x86 CPU on the same SoC, and have an ARM/GPU SoC for the handheld and an ARM/x86/GPU SoC for the home console. It's a little crazy, but hear me out: ARM had great support for co-processors. Something as ubiquitous as a CPU's MMU is a co-processor on ARM, at least pre-ARMv8. After ARMv8, the MMU was integrated with the CPU and coprocessor support was phased out, so Nintendo would have to add it back in. Other components like USB controllers, etc. would be separate chips from the SoC. In both cases, the OS would run on the ARM CPU. I've looked at die shots for all the 8th gen consoles, and all 3 use ARM CPUs as part of their security during boot time, so it's not totally far-fetched. I'm not convinced that this isn't a terrible idea, but it seems, at the very least, plausible.

Nintendo won't touch x86. If they wanted to go that route, they would make a conventional console, and this sounds like anything but. They will use ARM.

If it can be done through some dev tools instead of emulation, then it's even better. And AMD is in a good position to deliver both kinds of APUs.

@Soundwave: Going with an x86 processor doesn't go against exploring new oportunities. And look what happens with the PS4 and X1, both consoles have an 8 core x86 CPU processor that is more powerful than any ARM solution out there and despite that, they are both CPU limited. If Nintendo goes with an ARM processor for its home console, the kind of games it will be able to run will be limited.

Logical inference about NX I am gathering based on posts, articles, steaments and rumors.

1. Nintendo is most likely going to be building a budget console of around $200 - $250 and around 200 for their handheld
2. Powerwise it the handheld and the console version will be relatively close together, with the console version only somewhat more powerful.
3 Nintendo is likely to make their console and handheld have a common architecture and operating system. The customer will buy one version and get the other version for free on the other or perhaps be able to insert the game in both the handheld and the home version.
4. The next console will be probably more powerful than the Wii U, but probably less so than the xbox one. How much less so under the Xbox1, I'm not sure.

5. Nintendo will be using some kind of account based system managing games, offering deals, and giving online functionality  in their games

6. The online capabiliities will be significantly better than wii u but probably less so than the ps4 and xbox1, at least out of the gate. Nintendo has even stated that online functionality in games is becoming increasingly important to them. You can see this fact in games like Splatoon.

Based on other rumors I have heard, but am not so sure about.
1. Nintendo's next hardware will have some kind of android functionality, to what degree is still up in the air.
2. There will be some appeasing of 3rd parties to make their games easily ported over to the new systems, but to what degree, I am also unsure. I also don't think they are going to be bending over backwards for 3rd parties because they are unreliable and have been burned in the past. I think Nintendo figures they will have enough output for their games because they are now building one game for 2 systems. They can also leverage their handheld base and home console, so maybe they figure that 3rd parties will eventually come because the combined install base are simply numbers that the 3rd parties cannot ignore.

Also, will they be charging some kind of monthly online fee to be able to play online like Microsoft or Sony. I'm betting on no because again they are going to be building a budget console and want to keep the price down. Their hand in the market is not strong (the wii u selling only 10 million so far and a shrinking handheld market), so they have to take a more pro-consumer stance. So the question would be how do you get more online functionality, while keeping it free.

What will the amiibo functionality likely look? I doubt they will can the idea because that has been their most successful idea this generation. Will it be increased or stay the same? Will previous figures work with the new system? 

How will will it communicate with ones PC and phones? 

How much of their mobile strategy will affect their new console and handheld?

What will the release schedule look like? Will they be releasing a handheld and console variant at the same time or will it be staggered? I'm more incline to say at the same time.

My own thoughts:

1-Agree on the console but not the handheld. I think $180 is more likely.
2-We don't have any details on that, so I'm just going to say that I hope they are not. A $250 console can be a lot more powerful than a $200 handheld.
3-Yes, I agree. Nintendo said that they would share the same arhitecture and the OS could be based on Android as some rumors have said. But the part about buying one game and playing on any NX machine... well, with Nintendo you never know. They could launch 3 SKUs for their games: handheld, home console (both same price) and both, with the latter being $5/10 more expensive.
4-Again, we don't have any details on that, so I won't say anything.
5-That's for granted. After all, this was one the claimed reasons to go with DeNA, to help them develop an account system.
6-Agree and, merging it with your last section, I could see Nintendo going for a Live like system with some functionalities being free (one of them online play) and others reserved for paying customers.

I believe power wise that the handheld and the console will be failry close together spec wise is because that's the only way they will be able to port their games onto both systems extremely easily (at least according to Iwata to have them be brothers in an ecosystem much like how apple does their products. You can't take a ps4 game and port it onto a ps2, hell you can't even take a ps4 game and easily port it to the ps3. Even with pcs for the newer games, even if you drop the resolution down to 720, and minimize a lot of the other game settings, the game will only play within a certain range of machines. I believe at most, the handheld can only be about a half generation behind the console in terms of power. So when the NX comes out and you get something that is considered like ps3.5 powerwise for the console(xbox1 seems like the equivalent of about a ps3.8 on the spectrum), the furthest back the handheld would be is a ps3. The Wii U is probably more like a ps3.2. So powerwise the console may be somewhere halfway between the wii u and the ps4, and handheld will be about as strong as the wii u, if you go by how Nintendo has done their previous handhelds.

They'll be like brothers, not like twins. I'm seven years older than my brother (nothing important now but quite a difference when we were younger) and we are very different physically. Yet we have the same surnames and brown eyes. That's what I think Iwata meant to say with that comparison. Both devices will be "Nintendo" and both will share the same OS, something that would allow them to share some of its library. After all, not every iPad App works on an iPhone and viceversa, so there's no reason to assume that every game has to run on both devices.

And despite what it looks like, very few Nintendo games can be considered taxing on the hardware side. Don't get me wrong, they are very pretty and their art style makes them stand above the competition (both in their machines but also compared to their competitors offerings), but they generally don't make their hardware sweat.Take the last Smash Bros as an example. It's the same basic game on both versions just with the graphics adjusted down for the 3DS. And that's with a machine that's not more powerful than a Wii and another one that's more powerful than a PS3/360. And with completely different hardware.

Is there a reason why Captain Toad couldn't run on the 3DS? Kirby, Yoshi, Pikmin, Donkey, Wonderful 101, Mario Kart or Tennis...? There are lots and lots of games that look great on WiiU that could run on the 3DS (Hyrule Warriors being the latest example, though that's not a Nintendo game). And on the other side, there will still be games that would be impossible to port from WiiU to 3DS like Xenoblade X or Bayonetta, but there are also 3DS games that while could run on WiiU, they don't fit in a home console.

And that's the way Nintendo should go: launching those brother-like machines that can share 90% of their games library but that also offers something unique for the ones that prefer playing on the go and for those that prefer playing on a TV.

And the usual Third parties talk... well, by now Nintendo should have realized that they can only count on themselves, so while they shouldn't close the door to Third parties, what they should do is consider their own needs first and then, if the others want to come onboard, welcome them.

Sigh, I swear this company is run by 100 year old people.