I've got a d600 and a d810, so fairly representative of the two you mention. My d600 never gets used anymore as I find the d810 so much better.
They both produce fantastic images, IQ and dynamic range on both are supurb. So good that they are the among best sensors on DXO.
The reason I prefer the d810 so much isn't due to better IQ (it's sharper but not enough to warrant an upgrade), but it's build quality and ergonomics. It's a pro build camera, whereas the D600 is very much a consumer built camera.
The file sizes are massive on the 800/810, a raw file opened as a TIFF in Photoshop is 206mb!
However this does allow a lot of cropping if that's your thing.
I wouldn't say the 800/810 is that much better in low light, however the autofocus system is night and day better.
If IQ is the only reason for your upgrade, I wouldn't bother.