Nice review Graham, I think you hit the highlights of the camera well. One correction, the 6D doesn't have the same sensor as the 5DmkIII, the 6D is 20mp vs. 22mp on the 5DmkIII. The actual difference in IQ is minimal, they are in essence equal cameras in terms of the sensor.
I have both, and enjoy both. The 6D is the newer camera for me, having used it now at 2 weddings I've grown quite attached to the camera. At first I wasn't sure about it, but the one thing that did appeal to me was the additional sensitivity of the AF sensor, and I've found this to be quite pleasing in practice. For those dark receptions, the camera locks on focus quicker than the 5DmkIII (which is no slouch, except in extremely dark conditions). I have yet to find a situation where the 6D has been unable to attain focus. Also, even though it's primarily useful as a center focus point only system, I've been finding this to be rather quick and uncomplicated to use this way. With the 5DmkIII, I am constantly trying to move the active AF point around, and find myself fidgeting with it quite a lot at times. With the 6D, using focus and recompose technique, I'm finding I'm actually a bit quicker in shooting, to my surprise. I've also started using it with the AF lock button on the back, and this technique is also proving useful. This camera is teaching this old dog some new tricks.
Also, a nice aspect is the viewfinder is brighter with faster lenses than the 5DmkIII is, the different screen in the 6D provides a nicer image through the viewfinder in this respect.
Over all, it's a very nifty and finely tuned camera, one that I find is actually fun to use, more so than the 5DmkIII in some respects. It just feels like driving a sprite little sports car, brings back the joy of shooting.
