To be fair, I think jrista posted two reasonable examples: one was the room interior with bright window, and the other was a stream with bright sky.
No one has posted a reasonable example. That would require both sensors shot so that all other factors are equal, and RAW files provided for everyone to evaluate. Since we do not have a 5D3 shot of the room nor a D800 shot of the stream we have no idea what the difference would actually be.
You, me, neuro, jrista, Keith...everyone here...none of us can accurately evaluate the luminance range of a scene by sight alone, nor the dynamic range of a RAW file, and compute in our brains how it might have looked on another camera. Not even close.
Absent that you get confirmation bias. Every Canon shot with a white sky or black shadow is due to 'Canon's crummy sensor.' Every Nikon shot with a good range from shadow to highlight is 'thanks to those amazing Exmor sensors.' Even if you could have swapped cameras and gotten the same results they are interpreted that way. Heck, in another thread we had jrista cruising 500px thinking obvious HDR images were single frame Exmor shots. Outside of this debate and the psychological biases it has introduced...one's frame of mind if you will...he would have never assumed some of those shots were anything but multiple frame HDRs.
We have plenty of words but no real examples save Fred Miranda's, and the difference there is simply not worth all these words.
I would love to put this to rest once and for all, but I either have to borrow a friend's D800 (which he's always using professionally) or buy a Sony A7 (which I'm planning but haven't done yet). But a half dozen threads on the same topic is pointless absent a series of "all other things equal" test shots. Real world test shots. Not black paper in a coal mine "I pushed this >5 stops and turned off all NR on the Canon and look at how much better Nikon is at 300%" nonsense.
Despite my clashes with jrista I would trust him to do this. His sunflower scene would have been a great test if he had only had a D800 to test. I suspect the noise would have been much better on the darkest frame, but the shadows would have been mud that deep. I could be wrong.
if you happen to be at one of these locations at that time of day, those two shots would benefit from the D8xx sensor.
jrista doesn't actually know this. Neither do you or I. You have to actually test both at the same scene. (Side note: based on what experience I do have processing/printing D800 RAW files I would guess there would be some benefit. I'm not convinced it would be visual, but simply less work in post. I can imagine in some cases that it would be visual, but I don't think it would ever be massive, i.e. you are still going to need and use GND filters and HDR.)