I took some time to shoot a comparison between the 1Dx and the 5D Mark II, I found a scene with similar tones, then did a 1600 iso shot with the same settings (default jpg)
It appears the 1Dx and the 5D II have nearly the exact same noise levels, which would make sense considering quantum efficiency is likley very similar.
Here's a back to back comparison of a 100% crop of the 1Dx and a 21mp 5DII shot resized to 18mp. The noise has been enhanced with a high pass filter for easier inspection with an identical setting on the final composite:
It's worth mentioning though that according to DxO Mark Canon lied about the iso sensetivity of the 5D Mark II, so iso 1600 is really iso 1093 etc, a huge dicrepancy to make the camera seem like it has better noise performance. So this potentially means the camera if it is less deceptive about it's iso is somewhat better. Also let's not forget that it probably has better dynamic range and low iso noise and perhapse it has less banding etc so it looks better at high iso.