The iPhone battery numbers are very misleading becasue they account for general usage, not continued gaming at 3+ watts. The iPhone 6 Plus dies after about 3 1/2 hours of playing a 3D game, the regular iPhone 6 dies at less than 3 hours 

http://www.trustedreviews.com/iphone-6-plus-review-battery-life-and-verdict-page-6

The easier way to look at it is to look at the Watts/Hour rating, which Apple also provides. The iPhone Plus battery is 11.1 wh (watts per hour), meaning if your game is consuming 4-5 watts/hour, the battery will be dead in just over 2 hours. 

You would need something more akin to the iPad Air 2 size battery (6300 MaH) and a 24.3 wh to have a high end gaming portable. 

A 3000-4000 mAH battery would be OK, but you'd basically be limited to about 2-3 watts max for the hardware (screen will probably consume another 0.5-1 watt/hour) if that's all you have as a battery. 

Well it will be certainly stronger than Wii U, Nintendo will probably aiming hardware for 1080p/60fps for their game same like they aimed 720p/60fps with Wii U, and for handhled probably 540-720p.

Its not about just playing handheld games in higher resolution on console, but also playing home console games on handheld. I personally dont like handhelds and I would very happy to play handhelds games on home console, also you have people that more preferring handhelds (Japan market), they will certainly play home consoles game on their handhelds. Also majority of games will be in one version (it want be handheld or home console game), just on home console you will play that game on TV with better resolution, better textures and better effects.

You still didn't answer on my simply question:

if 1700 mAh battery last around 4-5 hours in 3DS XL with two displays (one 4.9" and one 3.5") or 1500 mAh Wii U gamepad battery last around 4 hours on 6.2" display how exatly 3000 mAh battery would be to little for next Nintendo gameing handheld with probably 5-6" display!?

It would be fine ... as long as your hardware is only consuming 2-3 watts max. 

Which means graphics better than the Vita, but considerably below the Wii U/XBox 360. 

You'd get a processor similar to the Apple A8 (the vanilla one, not the A8X) which can pump out about 115 GFLOPS and battery life of about 3 hours. 

3000 MaH is nothing special. 

What Apple has been able to do with their phones through the software/hardware integration is bring down the power usage of tasks like web browsing, video viewing, and other general smartphone usage so they use very little electricity. But that doesn't work in the same way for intensive 3D video games, the iPhone still rips through battery when forced to play higher end games. 

I personally would ditch the 3DS form factor if neccessary and go with a more tablet style form factor. The battery and the resulting chipset you could put inside would be far superior providing a better experience all around. A 6000 MaH battery would be far more ideal. 

Frankly, Vita graphics are so much better than 3DS (I finding that even PSP graphics look better) that only Vita graphics for next Nintendo handheld would be huge improvement (probably biggest improvement for any Nintendo handheld), but maybe we can expect even better graphics with 720p screen.

Vita have 5" display with 2200mAh battery that holds around 4 hours.

And that's fine, but then the problem is where is your console in all this? 

If the handheld is 115 GFLOPS, lets say, you can't have a console that's like 1.5 TFLOP (15 times more powerful) and expect any kind of real meaningful integration, anymore than the Vita is able run even PS3 ports (it can't). 

That probably means a very low end console, which I don't see working out too well for Nintendo, especially with the AppleTV now coming with free-$10 games and a $149.99 sticker price itself. 

I think Nintendo is also keen on at least having Wii U level visuals on their handheld too so they can port games and quickly bring over existing engines to the portable so that can lead to quicker development times. 

The 3DS form factor isn't even that great to be honest, it's not like it's very pocketable at all. If push comes to shove I would let go of that form factor for the time being (a die shrink to 10nm in the future could open the door to it coming back as a pocket model) and embrace a more tablet like form factor. 

Actually thinking about it ... if they really were married to the idea of the fold-out style of the GBA/DS/3DS ... the way I guess you might be able to do it is have a large 3000 MaH on the bottom portion the handheld and another 3000 MaH panel behind the top display. That would give you a fair bit of battery power for sure.

I mean the top portion of a 3DS XL is already about as thick as a modern iPhone, so I don't think it would be that hard to fit a battery behind the display.

The way they could save money is to have a larger top screen display, but have it be able to swivel somehow to a vertical position, that way it could emulate the dual screen set up without physically having to have dual screens.

Interestingly enough I just checked and the Wii U tablet screen is exactly the same width when held vertically as the width of the original 3DS screen. I wonder if that's coincidence or if Nintendo testing that particular screen size for a reason. Still I think probably a tablet layout would be more preferable. 

I dont think that difrence in power would be a problem, beacuse of same arhitecture, with same arhitecure anything is possible, also I dont think that home console will be 15x times more poferful than handheld.

For instance Vita and PS4 have solid integration and even dont have same architecture and power gap is huge, also Sony did not aiming for heavy integration with PS4/Vita like Nintendo is aiming for next platform.

Apple TV is basically Nintendo Wii in 2015. so I dont see Apple TV like competition for NIntendo.

We still dont know what is Nintendo aiming in term of power, but I think Wii U visuals on 5" display would be overkill because Nintendo Wii U games look and work very great on big screen, so I really don't see those graphics on 5-6" display.

I am pretty sure that 3DS form factor will change with next handheld.

I think Nintendo using AMD's FinFet 14nm technology is the key. Maybe that's also why they've specifically been waiting until fall 2016, because really the 3DS honestly could have used a successor this fall as it's shipments are really slowing to a crawl and it will be 5 years old in a few months anyway. If they were just planning to use ho-hum tech they could've launched the portable NX at least this fall. 

If all they wanted was something 2x-3x better than a Vita for example, that type of tech is dirt cheap right now. 

Fall 2016 lines up perfectly with AMD's 14nm FinFET process getting large scale mass production. Same thing for AMD's HBM2 RAM (high bandwidth memory). Just kinda makes you go "hmmm". 

You're doing it again, using Flop ratings to compare multiple different manufacturer's technology, when Floating Point calculations are not an industry standard measuring metric.

No company measures them in the same way, so you using them like they are is completely disingenuous.

No AMD are not aiming for 70GFlops per watt, going by the way AMD measures FLOPs, at 28nm's they've achieved 819Flops over 35watts, that's taking everything together into account across a Carrizo APU/SOC, which means they've achieved 23.4GFlops per watt, if that architecture can be shrunk to 14nm it would achieve 46.8GFlops per watt.

Perhaps they can optimize their design to gain more performance, but that would take time, 2016 probably isn't going to be when they can achieve 70GFlops per watt at 14nm, maybe they'll get close to 60GFlops, but this is based on how AMD measures floating point performance.

GFlops are not a standard for measuring total processor performance, you using PowerVR, Nvidia's Tegra or anyone else's tech as a comparison, with GFlops as a metric makes absolutely no sense, ratings are not comparable.

Flops are a marketing buzzterm, a fake figure to make it seem like you have X amount performance, but it's not accurate or a figure that is commonly always used in exactly the same way, nor does it cover total processor performance.

Flops don't tell you Instructions Per Second (IPS), cache size, cache amount, Bandwidth, latency between components inside a chip or between chips.