So I finally got my 5D3 last week and I got around to testing it with my current flash, the Nissin Di866 II. I seem to recall hearing about 5D3 having trouble using the AF beams of the 580 and 600 speedlites. I don't have any of those flashes to give a comparison but I can say that the AF assist with the Nissin was very reliable in low light!
I've tried using the AF beam both with and without actually firing the flash and in both cases, the unit actually manages to find the target even in a pitch black room. Heck, I couldn't even see what I was aiming at! All my subjective testing was done using the Tamron 24-70 lens on the 5D3 and from what I noticed, focusing with the AF beam seems to be just a tad slower than focusing with sufficient light.
Are there any users of both the 5D3 and the Nissin flash that can confirm these? Again, I have no experience with the 580/600 so I can't do even subjective comparisons.