I haven't made any claims that need to be proven. You claim a thing, and I doubt that claim. If you want me to believe your claim, you'll have to prove it to me. I don't care whether or not you think I'm right, you're the one attempting to convince me to change my stance. Anybody could come in here and say the Vita is only 5x more powerful than the 3DS, or that it is 50x more powerful, and I would have no more reason to believe them than I have to believe you.

You're saying that the difference between the Vita and 3DS is greater than the difference between the PS4 and PS3, so I stand by my comment that that would be an enormous difference in power. A difference I don't see represented in the kind of games they can run -- even factoring 3x the resolution and higher-quality textures and lighting, I don't see "Xenoblade Chronicles times ten" on the Vita.

How would anyone be able to guess that?

I substantiated my claims, and you just said, "not uh, I doubt it." The facts are that the Vita has a theoretical output of 52 Gflops. The 3DS's gpu is something like 4-6 Gflops. That means the computational power of the Vita's GPU is, indeed, capable of 10 times more Gflops than the 3DS. Gflops are a perfectly fine measurement for the performance differences between consoles, at least relationally. You were contesting that in the same way somebody contests any empirical measurement, "you can't prove, therefore I don't believe it." You are indeed making a positive claim though, by stating, " I doubt the Vita is nine times more powerful than the 3DS" a claim which you can't support with facts or evidence. Yet when I present facts, you don't even try to dispute them. Also, don't humor yourself too much, I wasn't trying to get you to change your position, I was stating why your position was more likely not going to happen for the instance of a debate on a public forum in which there are dozens of people reading our posts. It is for the reader that I defend OUR position (the people in this thread stating Nintendo in response to the OP) who you seemed so sure were wrong. 

I think it is important to not misrepresent my position: the percentage difference of the Vita and 3DS is greater than the percentage difference between the PS4 and PS3. This is not the same thing as the absolute difference. 

Absolute Difference: 52 Gflops - 6 Gflops = 46 Gflops.  

Percentage Difference:  52/6 = + 866%

Absolute Difference: 1.8 Tflops - .230 Tflops =  1.57 Tflops

Percentage Difference: = 1.8 Tflops/.23 Tflops = + 780%

What does Xenoblade Chronicles times ten even mean? That isn't how graphics work, anyway. There is a thing called the law of dimishing returns. In this context, it states that the marginal change in graphics requires an increasing marginal change in computing power with each advancement. It is precisely why the PS4 and XBO's GPUs only have 5-8 times more the computing power than their predecessors, while said predecessors have 12 times and 32 times the computing power of their consequent predecessors. This doesn't mean the games look 12, 32, 5 or 8 times better (if we can even quantify such a thing.) 

A few things:

I expect the PS4/XBO to release in 2018. Want to make sure we agree on the year before anything else. 

It has been the case that each generation the theoretical FLOP percent increase has decreased each time. For example, the XB -> XB360 was about 12 times, while the XB360 -> XBO was only five times. The PS2 -> PS3 was about 35 times, whereas the PS3-> PS4 was only 7.8 times (1800/230 Gflops.) So I think the trend of lower marginal increases in GPU power for the same marginal cost will continue and we're only going to see like 5-6 times percentage difference in 2018, especially when we consider how long last generation was compared with the sixth generation and what I predict the eight generation will be. 5 * 1300 = 6500 Gflops, 6*1300=  7800 Gflops, 5*1800 = 9,000 Gflops, 6*1800 = 10,800 Gflops. So unless MS/Sony decide on more expensive/more power-hungry consoles like they did in the seventh generation, I just can't see them going above 12 TFLOPs. 

As for native 4k resolutions, I don't think either Sony/MS will do it next generation and I don't think third parties are ready or want them to do it. The asset qualities at 4k would just be too high for them to keep up with the development costs. I think we'll see 1600p/1440p as the standards, much likes how sub-HD/720p was a standard in the 7th generation. 

2018? Depends on TSMC. Apparently, they should have 16nm in Q2 2016 (at least according to nVidia), knowing them that will be more like Q4 2016, so their roadmap with 10nm in early 2017 is...well, bit optimistic. But if they have mature 10nm by end of 2017, then maybe 2018 is possible, though I don't think that would make much sense for either MS or Sony, unless MS decides to do what they've done with original Xbox and kill it earlier.

As for this gen's jump - when you take how long 7th gen was vs how much of jump we have, both MS and Sony were very stingy. Sony just had to be carefull due to how badly they had it with PS3 and MS being specially missguided by their Kinect/TV policies. Otherwise, we would see (at least MS) what EPIC asked of them, which is around full blown 7870 with 2.5TFLOPS - that case with proper cooling most certainly can handle that GPU, price would probaly be same as or slightly higher than PS4 (since they're willing to lose initially on console), and I think their sales (at least in US and UK) would be much better then they are now.

So, no, I don't think 5-6x is resonable estimate (specially given how this gen was already underpowered, some more, some less, from the start, and how much bad press they have for it), just like I didn't think (along with few other people around here) that was reasonable estimate for 7th to 8th jump either.

And while I doubt they will go for native 4K (since they would then really have to wait for 7nm and 20+ TFLOPS GPUs), going with 2560x1440 (or 2880x1620, which would be 720p to 1080p equivalent) would give them a lot of headache with upscaling and some bad press, so I think they will opt for anamorphic and/or temporal 2160p which will give better image quality with similar pixel count. But for that, they need at least PS3 to PS4 jump.

Sirrus

Well my 2018 estimate depends greatly on when Nintendo releases their next console (which is looking to be late 2017.) It also depends on the capabilities of the PS4/XBO. By late 2017 4k display adoption rates should be quite big - enough to justify new consoles releasing in late 2018. As you said, this generation was relatively underpowered from the start. They're going to want to upgrade sooner rather than later to satisfy developers and third parties. 

Even if we consider that MS and Sony gimped their consoles for other reasons (if the cost is truly miniscule I don't believe Sony wouldn't have gone for a 7870), a 7870 would only mean a flop increase of 10 times, although it definitely would've given 1080p gameplay with a consistent 30fps. This is still much less than the preceding generation difference. I'm suspicious though of how cheap it would've been to go with a 7870. It seems to me that the additional cost would be between $50-100 (considering the retail price differences were double for a time after peak hardware development) and I'm unsure if that price difference could be reconciled with the XBO matching PS4 prices. It's not like these consoles are selling for a profit in their current form. 

Well we were talking about floating points. The PS3 was rated at ~230 gflops and the PS4 at ~1,800 gflops. That is a difference of 7.8. If the real-world difference is about ten times that, it is likely because of fewer memory bottlenecks and advance feature-sets. The same could apply to the PS5/XBTWO vs. PS4/XBO. The trend has been, with each geneneration, smaller increases in raw power/same price. This is especially evident when we consider how long last generation was. I just can't see the difference being much larger than 7th -> 8th generation, even if one of the manufacturers tried to outpower the other. I also don't see MS/SONY repeating the seventh generation power struggle. That was bad pretty much for both of them and third parties. 

Either way, I don't see native 4k being a thing next-generation (although I do think they'll try to promise it.) 

I think since the lower powered idealism for the Wii U hasn't worked out so well it will certainly be Nintendo. X1 and PS4 will certainly be decently powered units as well but the Wii U has the biggest jump to be able to make in contrast.

If its not Nintendo I will be incredibly disappointed.

Honestly, I'm not so sure MSony care at this point when will Nintendo lauch their next home console, at least not too much - unless they susprise them and have something that 3rd parties like a lot, or if we have another Wii-like craze, this gen is pretty much showing how important 3rd party support is and what will their audience buy. So, I'm thinking 2018 is bit too soon, 2019 seems more realisitic - again, if MS decides to pull original Xbox, and cut One early, that will force Sony's hand as well, but, tbh, I think a lot depends on TSMC in the end.

As for 7870 - well, IIRC, PS4 has one inside, it's just 2 CUs are disabled and and it's running @800MHz instead of 1000MHz (I remember back in days few of us disccusing 7970m, which is 7870 for laptops @850MHz as being possible choice for MSony). I'm pretty sure if Sony was in better shape for this gen (price-wise), they could've gone with worse yields (since at the end that's what 2CUs less is about) with bit higher price, but it seems price was crucial in their strategy . But obviously Sony ninjas informed them that MS screwed up XBO design, so they didn't have to worry. ;)

4K pressure will be interesting to see - SD to 720p pixel jump is 3x, 720p to 1080p is 2.25x, and 1080p to 4K UHD is 4x. While this does not mean that 4x more GPU power is needed (1080 to 4K is around 3x according to benchmarks), it's really a big jump compared to 7th to 8th gen. Who knows, maybe they will wait for it, but I doubt it - to have same relative jump as in this gen they would need really beefy GPUs.