So you're using auto ISO -- that's what I wasn't clear on since that means everything wasn't set to manual. As I said earlier, it already been demonstrated that the 5D3 produces a brighter image with the exact same settings at the 1DX. If you set everything to manual (including ISO) with the exact same settings, the resulting image will be brighter on the 5D3 than the 1DX.
The real-world application of this is that with a fixed shutter and aperture, you can shoot a properly exposed image with a 1DX and the same properly exposed image on the 5D3 will have a lower ISO. So when it comes to comparing high ISO image quality, it's not a valid comparison to look at the same ISO side by side. In real-world shooting you would need to compare a 6400 1DX image with a 5000 5D3 image. This I believe is exactly what you showed in your testing. Given that balance, the 1DX may not have any edge in high ISO over the 1DX. I've heard someone propose Canon did this on purpose to give the 1DX an apparent edge in high ISO.
Ok Chris, I understand you now. Got it. I agree, probably no real ISO advantage.