----This is a hypothetical situation, but the outcome is pretty odd-----
Okay so here is the situation, Assume that in this rig, our APU can utilize all of the RAM in the system.
Rig A has an APU
Rig B is similar, but has a dedicated GPU that is faster than the on board graphics of the APU, but it is stuck using 2 gb of VRAM, whereas the APU has access to lets say 8 gb (about average) of admittedly slower RAM
The result of this could be that Rig B does better at lower resolutions, but as the resolution increases, it's performance relative to the APU decreases. This is because it does not take as large of a performance hit from the increase in resolution, which hurts the faster but lower capacity card more.
Once the resolution reaches a certain point, Rig A outpaces Rig B
I know there are some problems but I think a situation like this might be possible under the correct circumstances.
We've already seen GPUs held back by memory. One of the major differences between Nvidia's 600 series and the 700 series was architectural improvements to the memory.
2GB of Vram is actually very appropriate for 1440p, but 3GB is preferable. It isn't just the amount of Vram that determines high resolution capability. The GTX 760 is a lower performing card than the GTX 670 at 1080p. The 760 is the replacement for the 660ti. However, the 760 performs faster at higher resolutions in comparison to the 670 - they share the same amount of RAM.
The APU with more RAM isn't going to faster because of the amount RAM it has. If you place 64GB of RAM in a system with an APU, the APU isn't going to use 64GB of RAM for the integrated graphics. That isn't how it works. Much like the 4GB variants of the 760 - the 760 isn't powerful enough to use it.
You said it yourself. The dedicated graphics card is faster. Vram is usually pretty well balanced with the performance of the GPU, for tasks that the GPU is geared for. If you take a 7790 2GB edition, it has no performance advantage over the 1GB variant whatsoever. So by the time the similarly performing dedicated GPU starts to run out of juice, the APU will certainly run out of juice too.
So I would disagree with you in the sense that an APU would get faster at a higher resolution because of the "amount" of Vram. Especially if that RAM is a lower clock less efficient generation. But like the new R9 cards, we can see cards gain performance benefits at higher resolutions in comparison to other cards. Because the 290x is geared for 4k, it will typically beat the 780 at 4k. Though, we see the 780 win at lower resolutions - if we consider the overclocked benchmarks that Linus posted on YouTube.
Linus and tomshardware always recommend nvidia and intel, for a pretty long while now, even though the competition has better options at the same price. They say they aren't fanboys, acknowledge the fact that AMD make good cards as well, but add in the end something about power consumption, noise or anything irrelevant since the cards they compare with are already huge power hogs and noisy as hell, like you're gonna mind that when playing games with sound...
The fact that 290x is better at a higher resolution and drops below 780 on lower resolutions is just because the games that they've tested work well with nvidia for a number of reasons, one of which is optimization, this means that the amd card is simply more powerful, but doesn't have proper drivers yet. Nvidia wants to guarantee you that for an ammount of money you're gonna get x performance, no freaky variance, no more, no less.
No. DRAM is much slower than GDDR5. It would be choking on the 4K buffer.
In any case, APUs will always be not as strong as a dedicated GPU at 4K. The reason being is that you can't fit as much CUs as a dedicated GPU chip can. Additionally, even if you increase the size of the die, it would get real hot real fast.