It is quite possible that each camera performs better in some specific low light situations than the other, and I think that is the case with these two specific cameras.

Low light performance is a pretty general term.

Usually when someone talks about low light performance they are talking about how much or how little noise is present in an image shot in low light. But that is still a little nebulous. Are you talking about shooting long exposures of stationary scenes at low ISO? Or are you talking about shooting shorter exposures of moving subjects at higher ISO settings? In the first instance read noise at low ISO is the primary concern. The Nikon D800 wins here. In the second instance signal to noise ratio at high ISO is the primary consideration, and the Canon 5D Mark III wins there.

As this long and highly technical answer to a question regarding dynamic range explains at length, there is more than one kind of digital noise. In the third paragraph from the end the comparison between the D800 and the 5D Mark III are highlighted. Because of the differences in how the two cameras makers approach noise reduction, Nikon does better at low ISOs where the primary concern is read noise and Canon does better at high ISO where signal to noise ratio is of greater concern.

Are you talking about auto focus performance in low light? With what kind of lenses? The Canon 5D Mark III shares the best AF system of any 35mm format DSLR in the world with the Canon 1D X, especially when using lenses with apertures of f/2.8 or wider. This is because some of the focus points in that system are tuned to work at f/2.8 where they can be more sensitive and more accurate than focus points tuned to function with lenses having a smaller maximum aperture. Canon is very open about which focus points are sensitive at which f-numbers. Nikon is more secretive at this point, but it is generally accepted knowledge that focus points in Nikon DSLRs are tuned to work with lenses that have a maximum aperture of f/5.6 or even f/8. So if you plan to shoot in low light with wide aperture lenses the Canon AF system will probably perform better than the Nikon. If you are going to shoot with slower zoom lenses, this may not be the case as much.

Both are awesome cameras with excellent low light capabilities. You can't go wrong with either one! I know working pros who regularly use both. They feel the Nikon does better at low ISO/long exposures and the Canon does better at high ISO/short exposures in low light. The exception is astrophotography, where even at low ISO/long exposures some Nikons tend to eliminate very dim stars as "noise".