I find this perplexing. Comments on this site and others from 5DIII users have led me to believe that the 5DIII shows some significant improvements over the 5DII in noise levels at higher ISOs. So, when you say the 6D uses "the same tech level as the 5DII/5DIII sensor" which sensor are you talking about?
The sensor hasn't been improved much on the 5d3, but the readout is cleaner (less banding) and the noise has a "nicer" film-like pattern giving it an edge on iso3200+ ... overall it might be a 0.5 stop improvement with a much more usable iso12800, but "significant improvement" isn't the word that comes to my mind here. The improvements of the 5d3 lie everywhere else, but Canon chose to reserve their best current sensor tech for the 1dx.
I can say that because I d/l'ed 5d2 and 5d3 raw studio samples myself (and so should you!), had a look at them in LR and up to iso1600 there is no difference I can see - some even figure that the 5d3 has worse sharpness than the 5d2 due to a stronger aa filter and it does have a bit less dynamic range (not that anyone would notice, but still...).
If people say the 5d3 is the high iso king imho that's because a) Canon marketing owns them, b) you see what you want to believe after paying $3500, c) the subjective impression how much less banding when raising shadows and the film-like noise pattern improves the picture varies among viewers and individual shots.
Last not least: Even if the iso noise on the 5d3 is somewhat improved, this even more shows the limited dynamic range of current Canon sensors that decreases further the higher the iso setting is. Disclaimer: The 5d3 is a great camera and I still didn't get a 5d2 because I still struggle with myself if I am willing to pay €3000, but the 2 stop improvement Canon predicted is a fairy tale.