Pixel size does come into it as well and can muddy up the comparisons for sure. But the basic here is the difference in surface size that is collecting light irregardless of pixel size. A full frame sensor is simply larger and therefore collects more light.
There is a Wikipedia article about this and modern sensors with more efficient circuitry have tended to minimise this difference in some instances but still there is usually a difference. Especially when pixel size is the same.
Full frame sensors often have larger pixels as well which also gives an advantage.
This article touches on it but the Wikipedia was very specific about sensor size giving a 2 stop advantage. If I can find it I will post it.
http://www.gizmag.com/camera-sensor-size-guide/26684/
I also agree his analysis may be flawed as I have not read any reports about the 7D2 having super low noise at high ISO rather what I have read is it is better than the 7D but not massively so in the noise department. Certainly it would be worth verifying from owners rather than racing out and buying one instead of a 6D and being disappointed later.
http://www.dpreview.com/forums/post/54846228
Greg.