Apart from anything else you might have heard, the 50mm 1.4 is £279 for both Canon and Nikon from WEX (as a comparator). But if I owned either a D800 or 5dIII, I'd get the Sigma Art 50mm.
The other thing I find troubling? The 5dIII is the camera most responsible over the last few years for people switching brands (Nikon to Canon). So I'm not sure you'd see the vast improvement you expect.
In the grand scheme of things, you can do what you like, it's your money. But someone would have to pay me to do the switch, enough to pay the difference and compensate me for the re-learning time.