I don't think they will go the powerful console route again, they did with n64, GC and the market punch them in the face. I would say it will be slightly below ps4 or even weaker. Perhaps it's a new handheld and they are quitting the home console market, which wouldn't be a bad idea

I was thinking of a rumor:

http://www.hardcoregamer.com/2015/07/04/rumor-nintendo-nx-will-not-be-as-powerful-as-ps4/157339/

I guess we will find out.

Below, for sure.

A more interesting question to me is whether it's weaker than the Xone, and if so then how much.

I think it will be a handheld, so below.

Below, because to do otherwise would require either of two things: 1) a higher price than the PS4, which we know Nintendo won't do, or 2) a much higher power consumption footprint than the PS4, which we know they won't do.

Third parties are sitting pretty happy at the moment with PS4/XB1 and PC using similar architectures, Wii U is the outer, not just in power but in the uniqueness of its architecture. If Nintendo want third parties on board, they need to develop a platform around a similar architecture, and provide similar dev tools, otherwise third parties will just ignore it again, especially because unlike the Wii where it really had 50% marketshare (forcing third parties to put something on it), the NX will be competing with a firmly entrenched PS4/XB1 and PC marketshare.

Assuming they go with a similar architecture, they more or less have to go with AMD as Intel 1) isn't interested in super low margin consoles (which they've said before) and 2) don't have the necessary GPU tech with which to integrate into an APU (sufficient to match PS4/XB1). To not have an integrated APU would increase cost and further reduce their ability to compete.

Going with AMD, at best they can go with Puma cores and an updated Radeon, however to be cost competitive with PS4/XB1 it can't be any larger than the existing PS4/XB1 APU's, which currently is ~330mm2. As the NX APU would be manufactured on the same process as the PS4/XB1 (because they'll be made by the same people, TSMC), to keep within the same size means keeping the same transistor budget. Contrary to what someone in this thread said, Puma is not expected to any faster clock for clock than Jaguar (they have the same architecture), and it has the same transistor budget. What it improves is energy efficiency, which may allow Nintendo to clock the NX APU higher but we aren't talking 40%, maybe 20% higher max. Improvements in Radeon performance have scaled pretty linearly with transistor count, so it is unlikely that AMD will be able to improve NX's GPU without increasing transistor budget (and cost).

So in a nutshell, with PS4/XB1 being based on very low margin high volume hardware, there isn't much room for design efficiency improvements whilst maintaining a similar system architecture in order to get third party support. Therefore, if Nintendo want to be cheaper than the PS4, then the NX will need to be less powerful.

Puma is an evolution of Jaguar, just because it uses a 28nm process that doesn't mean it can't have improvements, because AMD re-designed the layout of the chip, to add in more transistors within a smaller area on the same fabrication process.

Another factor is power management, AMD also added in features that power down areas of the chip not in use, which means less power usage, hence why Puma could clock 4 cores up to 2.4GHz at 15 watts, Jaguar needed 25 watts to do that.

Partly this is down to improvements in power leakage, but also improved architecture.

Puma and Jaguar are architecture names, which should tell you they're different and not the same, the designs are different too.

Also as far as your comment on costs goes, you're wrong, more power doesn't have to mean more expensive, in fact improvements in design can actually allow for more performance at less cost, fabricators also optimize their manufacturing which means less wastage.

Newer tech, within an even more mature 28nm process will be available to Nintendo, this includes CPU, GPU (which AMD have also made improvements within the same 28nm process) and memory will all be available to Nintendo.

For one thing 1GB GDDR5 chips are available to Nintendo now, using 8GBs from the get go if they want, or HBM and DDR4.

We all want it to be stronger but we all know its going to be weaker.

Yes, architectures can be improved, but to date AMD has made very little mention of performance improvements with Puma other than performance per watt, which I already discussed might allow higher clocks but we aren't talking huge gains there. The bulk of the APU's power consumption is from the GPU side anyway, not the CPU side, so even a 50% more power efficient CPU will not significantly improve the power consumption of the overall APU, and its the APU's overall power consumption that dictates what clocks the chip can support.

Regarding 28nm maturity, TSMC 28nm was released late 2011, it was a mature process when the PS4 released and its not expected to significantly improve from this point on because its so mature, nearly unprecedented how long the industry has stayed with 28nm in fact. 1GDDR5 chips are available (and in use) by Sony already, and therefore helps Sony reduce cost just as much as nintendo. Outside of a massively new technology coming on board (HBM for instance) whatever can help Nintendo helps MS and Sony, thus preventing Nintendo from achieving higher performance at a lower cost. HBM is definitely an opportunity for Nintendo, but its not cheap by any stretch and I am very sceptical that it will fall within Nintendo's price range by 2016 when the NX releases. 

youre better off thinking of it as wiiu 8th gen attempt 2.

It depends. AMD plans on having 16nm FINFet process APUs by that time, so it could use those. They won't use the new Zen architecture, but it will probably either by Carrizo (which is better than what's in the PS4 by a decent amount) or something slightly better. Don't know what that means for graphics though - they COULD get a lot more cores than the PS4 has, but it's up to them.