As has been requested, I did a quick amp glow / night scene test with the 5D3 and 1DX. While I still "have" the 5D2, it's wrapped in a shipping box ready to go to my buddy, and I was too lazy to go thru the exercise of unwrapping it (and mainly wrapping it again; how I squeezed the 5D2 including RRS L-plate into the original box shall always remain a mystery).
With each camera I took four exposures at 3 minutes and one exposure at 6 minutes, at different ISO (and aperture to compensate for it). Both cameras were running at exactly the same time, so that if the neighbors turned on the light it would affect both scenes equally. No type of in-camera NR was employed.
I think this must be the first time since ... wait, ever, that a 1D class body looks better in this test than the 5D of that generation (or any other "lesser" body for that matter). While I didn't do a parallel test with the 5D2, based on my experience I'd say that the 5D3 doesn't look any worse than the 5D2. Both cameras struggled pretty bad with the 6 minute exposure, or with the ISO 6400 scene. The 1DX did really really well at 3200 at 3 minutes, I'd say...
The subject matter is boring, just my back yard, with severe sodium vapor light pollution, but I was lazy and didn't feel like heading out to the woods. I understand that that's what it would take to get the really mean type of amp glow, but I suspect we would see signs of it even on non-black images at higher ISOs.