LPDDR4 is pretty decent as main RAM IMO. It is energy efficient and can get up to 50GB/sec these days which isn't bad considering. 

If Nvidia can give Nintendo a way to only need 10MB-16MB of eDRAM instead of 32MB, that wouldn't be bad. It will consume energy, but this is one area Nintendo is likely to splurge on because Nintendo simply loves their fast memory pools. 

If the 3DS has 10MB as is, it's unlikely the NX will have less. 

Unless Nvidia can provide a different solution or if Nintendo can maybe do something like a very, very, very small pool of HBM (only 10-32MB say), but I don't know if that would work. What consumes more electricity, eDRAM or HBM (out of curiousity)? 

I'll be interested to see how they handle this issue, this is probably the primary point that Nintendo has to customize the Tegra chip. Even a game like Zelda: BotW is likely highly dependant on having a very high speed pool of RAM, so the NX will have to have something in that regard I think. 

Not sure if you know how memory works. But 50GB/sec isn't happening, not in a mobile device or small form factor.

clock speed * (bits per clock/8)
3200mhz * 64/8.

You will likely get about 25GB/s on a 64bit LPDDR4 interface.
The reason why the Xbox One has such an advantage is because it can afford to have a much larger memory controller and drive everything on a 256bit bus.

Remember also that memory bandwidth and capacities aren't combined when you combine GPU's to process a game either.

If you go with 10Mb-16Mb of eDRAM, you are going to be limited, there is only so many "ways" you can do something effectively.
The Xbox 360 also had 10Mb of eDRAM and relied on a tiled approach, but it still limited developers in many ways.

Agreed. Not only that, but it would be pointless.
We also need to take into account the resolution and level of fidelity the 3DS is operating at, it's not breaking any records, something more modern with more effects will... Well. Simple require more.

With that said, one of the benefits that eDRAM could be used for is as an L4 cache, Intel has done this successfully and the gains for the CPU isn't to be understated either in some edge cases.

HBM would use more energy than eDRAM.

But it all comes down to how it's implemented and the size of the memory.
One of the advantages of HBM is how large it's capacity is verses eDRAM.

Doesn't the iPad Pro hit 51GB/sec? 

The A9X is paired with 4 GB of LPDDR4 memory in the 12.9" iPad Pro and 2 GB of LPDDR4 memory in the 9.7" iPad Pro with a total bandwidth of 51.2 GB/s. This high bandwidth is necessary to feed the SoC's dodeca-core PowerVR 7 Series GPU cores. The RAM is not included in the A9X package unlike its sibling, the A9.

If eDRAM consumes less power than HBM, that's probably what Nintendo will use again, I think, they will try and work with Nvidia to get that size down from 32MB though. 

If I had to guess, I'd say maybe 4-6GB LPDDR4 (1GB reserved for the OS) for the main RAM with 12-24MB of eDRAM. 

Not sure if you know of Apple, but they tend to have strange way of having power efficiency that all other platforms seem to be incapable of, besides that iPad has the space for a chunky battery as well.
It's also a far more expensive device than a console at $1250 AUD for the base model so they can afford to implement a 128bit memory bus
and at 12.9" you are likely to have more space to implement the extra chips and traces that you wouldn't in a more conservative size.

We also need to put things into perspective here.
Nintendo essentially needs to build a Tablet with built in controllers, good screen. etc'.
And then (If people's opinions/rumors are true) a dock, all for under $400, only so much you can do, Nintendo can't go all-out on hardware if they need to worry about things the competition doesn't. (Dock, Screen etc'.)

I think 4Gb is the sweet spot at the moment for most SoC's, having 6Gb of memory would come with it's own caveats (Some impacting performance.)
Or they will go all out on 8Gb, which I would prefer at a minimum.

The main cost of the iPad Pro is that monstrous super high resolution 12.9 inch display though. The actual A9X doesn't cost that much. That and Apple likes huge margins on their products of several hundred dollars. 

Nintendo could use a much cheaper 720p res and smaller screen. The Wii U tablet in physical volume is actually bigger than an iPad Pro I think, the iPad Pro is huge, but it's razor thin, a Nintendo "tablet" will have to be thicker for comfortable gaming sessions so that's a bonus there. 

Batteries are fairly cheap too, a 10,000 MaH battery can be had for dirt cheap even at retail, the manufacturing cost of them is maybe like $5-$8 a pop. 

Memory is one area Nintendo I think will splurge on though. They are a bit anal retentive about memory, I think after the N64, which used a memory type they hated, they've focused more on that aspect. 

Gonna have to spend on memory. The Tegra SoC though I bet they are getting for a steal. $50-$70 for the main chip, $40-$50 for a 7-8-inch low res LCD + touch panel, $30-$50 for your memory, $50 for misc (WiFi, motherboard), $10-$12 for a small pool of flash RAM (32GB?), $8-$10 for your battery, also no need for super high quality cameras, Nintendo could go for cheap there ($2-$3 total), etc. 

If Nintendo goes for a 720P screen, then they don't need more bandwidth.
I would prefer a 1440P screen, but they aren't cheap, my Phone has a 1440P screen, so does my computer, it's the minimum for me these days, but I tend to be on the fussier side of the fence. :P

And the reason why the iPad has such bandwidth isn't limited to just the resolution either, the SoC for instance doesn't have any L3 cache, so bandwidth becomes a larger importance.

As for battery's... You have battery's and then you have battery's. Nintendo can't just pick any random cheap battery, we don't wan't devices catching on fire or exploding, they have a degree of quality they need to ensure.
Besides, space, usually larger capacity battery's need more space, The NX isn't going to have the same amount of space as an iPad 12.9".

What type of bandwidth do you think they would need for a 720-800p display?

1440p obviously ain't happening. I have a 1280x800 resolution 8-inch Samsung tablet and honestly the display is pretty nice. Waaaaaaay better than the Wii U or 3DS screens, and I think I like it better than the Vita even, and t his was a dirt cheap $150 tablet that I got two years ago. LCDs are really dirt cheap these days so that's one benefit to Nintendo. 

Is there some reason why the iPad couldn't have a L3 cache? I think Nintendo could use a similar main memory setup for the LPDDR4 RAM, but have eDRAM on the die, that would be pretty good, no?

Batteries are still ridiculously cheap for manufacturers, even the highest end, big phones, the battery is like $5-$8. 

The NX is going to have to be big, that's just how it is, but even a Vita is almost 3x the thickness of an iPad Pro. If NX is the same thickness of a Vita, but is the physical dimensions of say an iPad Mini (height x length), then that's basically like three iPad Minis compared to an iPad Pro ... or basically take your height and length and multiple by three. 

There should be enough space for a monstrous sized battery (10,000 mah, maybe more). 

I wonder if this patent would hold up if contested?  Off the top of my head, one "prior work" example is the Microsoft Surface Book.  Some Surface Book SKUs contain a discreet GPU in the keyboard that the tablet docks to.  Yes the NX is a handheld game console, and its dock is for a monitor, but is that enough of a distinction for a patent?  I'm no patent lawyer, so I would love for people in the know to chime in.

Nintendo sought a patent for a game that plays itself but lets you jump in and take control at a point of your choosing, despite the fact that the CD32 version of "Defender of the Crown" had that exact feature well over a decade earlier, but Nintendo probably didn't know that.  I wonder if this is another case of Nintendo filing a patent despite being unaware that it had already been done in a related fashion?  The Surface Book screen is a portable device, and the discreet GPU is definitely promoted with gaming being a reason for its existence.

Yeah, of course Nintendo will launch a much more powerful handheld than the n3DS for $149... These expectations are hilarious!

They still sell their n3DS models for more than that.

Google Pixel C might be a good comparable. It has a Tegra X1 processor at 80% of full clock, at dimensions of
9.53 in x 7.05 in x 0.28 inch deep. It also has a monster 9243 MaH battery (32 watt hours).

But lets assume NX has similar width, bring it down to about 9.5 wide, but it's not as tall since it doesn't need to have a 10 inch display ... so lets say 4.8 inches tall, but similar thickness to a PSVta, which is 0.7 inches ... the added depth would make a huge difference it effectively more than doubles the internal volume.

If the Google Pixel C was 2.65x as thick even if you reduced its height, likely the Tegra could full clock.