Those camera size comparisons are very misleading ... in reality there is a significant difference in the space that a 6D+24-70 f/4 & a7+24-70 f/4 occupy in the camera bag. In the space that 6D+24-70 f/4 occupies I can fit in an a7+a6000 cameras and 24-70+10-18mm lenses.Have you ever hand-on a7 series with their native lenses: FE 35mm, 55mm, 24-70mm etc...?
I did try the A7 at my local photo supplier when I was considering this option, but I did not test the whole set of native lenses. Although you're right that these are smaller than Canon's L equivalent, I did not find the size/weight reduction significant enough for me to step out from my 6D+ L lenses system (sure, the difference would be much more striking with a 1D body).
Your comment made me curious enough to dig the aspect of size difference further, and here are some side-by-side comparisons (keeping the equivalent focal length and apperture as constant as possible) :
¤ 35mm prime (135 format): http://camerasize.com/compact/#380.368,487.394,520.422,ha,t
¤ 50/55mm prime (135 format): http://camerasize.com/compact/#380.306,487.87,520.408,ha,t
¤ 24-70mm zoom (135 format) range: http://camerasize.com/compact/#380.367,487.393,520.421,ha,t
In some cases (like with the 35mm prime) the Sony system is indeed very compact and even smaller than the Fuji X, but in other instances the size difference with the 6D is very limited. Now, what would be interesting is to compare how the Sony lenses fare compared to Canon's L in terms of optical quality. That could be something to do on DxOmark next time I have time for that.
Interesting on the camera comparison. The site only show top view? I wonder, why don't they show front, back and side view