Here's the thing....even if Nintendo had the most powerful console would the majority of players buy the console to play AAA online games?
Online friends are a big factor in online games for many people. Right now I have ZERO online friends for any Nintendo console so what would be the incentive for me to buy this hypothetical Nintendo console? Sure it will have slightly better graphics than SONY's and MS's console for multiplatform games but it wouldn't have AAA exclusives like those two consoles. Why would I buy the Nintendo version of a multiplatform game that my friends play on a SONY or MS console?
The only way I could see this working out somewhat well is if they had the most powerful console
and AAA exclusives. I can't see EA or Activision or any of the big software companies release AAA exclusives on a Nintendo console...not even timed exclusive. I just can't see these games selling better on a Nintendo console than a SONY or MS console. When you look at 1st party AAA exclusive games on SONY and MS consoles they are usually pushing the envelope...I just can't see Nintendo doing this given they don't have any IPs that benefit from that type of technology advancement. I guess the next Zelda and Metroid could be good candidates but I'm not really sure if Nintendo would actually push the envelope for those IPs.
There is another way, leveraging their Handheld and Console audience together, give developers 1 dev kit for both units (the Wii U dev kit is very cheap, and comes with unity so there is no barrier here for even small developers) If developers can code once to both platforms and simply change settings (yes including AI settings) to target both audiences, it would mean a more interesting target for developers, especially those multiplatform games that are going to eventually target mobile too (as the handheld will have average at best specs for this segment) That is how you make 3rd parties interested again. It wouldn't matter too much what the specs are, as long as the architecture is there and it is at least comparable to PS4 specs.
The above market would likely be bigger than either other console, so developers would have another Wii situation but with modern hardware where they don't have to jump through hoops. If you think about it, PS4 is going to be supported into 2020 most likely. Even if the PS5 comes out in 2018, this means Nintendo not only has a year start with their own box (at least) but that they can ride out PS4/XB1 ports, I'm not saying it's 100% going to work, but it's their best chance to really gain back 3rd party support.
They also need to increase their own title output by 50% (atleast) Looking back at 2013, Nintendo released ~25 titles across Wii U and 3DS in north america. 50% increase is ~38 titles a year, this would be a huge increase in output, and completely doable thanks to a move to 1 architecture, especially if that architecture is simply scaled. A lot of these titles could actually be applied to both platforms at the same time or within the same year at least. Mario Kart would be a title they should push to both platforms together, allowing cross play for their platforms would also be a nice incentive that they currently do not have. This doesn't include the exclusives they do get (such as monster hunter 4) but is an example of how they would be able to leverage both platforms to increase their content and also attract 3rd parties back. Between the 3DS and Wii U, there is over 50 Million users since March 2011. Both platforms sold horrifically in their first year as well, so I do like to think of this as the "Nintendo base" Something they can expect to exceed if they execute correctly with their next 2 platforms. This is something 3rd parties will look at and decide that it's just too big to ignore, especially when they can use the same engines they are already working with on these platforms. That is paramount to this all working of course.
It's not a full proof plan, but it is what Nintendo has basically said they are doing, if they use AMD's APUs it will be that much simpler to bring 3rd parties aboard, but they could achieve this in a Nintendo way by simply increasing Wii U's Cores, shaders and clock speed. (I do expect them to upgrade the GPU either way, the AMD component here doesn't look like unique hardware, it just has extra unique parts bolted onto VLIW5)