AF speed is a combination of the AF system, what mode it operates in, and the lens.
The 5D3 has 5 of its central AF points which work as dual cross type AF points with lenses having an aperture of f2.8 or greater. So I'd recommend staying well clear of anything slower than f2.8.
With my 5D2, 24-70 II and a Sigma 50/1.4, the results are about the same with either combo in low light. Even though the Sigma has much slower AF than the 24-70 II in good light, in very low light it seems about the same as the Canon when shooting stationary subjects. And when the light levels get so low that the Canon starts to hunt without being able to lock on, the Sigma gives up at that point too. However, to keep the ISO lower or gain faster shutter speeds, the Sigma 50/1.4 is my preferred low light choice.
What lenses can you choose from? You talk about an f4 lens being available, and I can't see an f4 lens in your equipment list - so while the Sigma 50/1.4 and 135L both look like the pick of the bunch, I'm guessing there are other fast lenses for you to choose from.
A bright lens with better AF than the Sigma (such as a 24 L II or even a Canon 50/1.4) should focus faster than both the Sigma 50/1.4 and 24-70 II in very low light. And as to how a 5D3, the lenses you've got available and the lighting/subjects all differ, that just all mixes it up and makes it next to impossible to give you a definitive answer. I'd suggest making an educated guess to pick a couple bright lenses which are known for fast AF from whatever selection you have available to you, and find out the answer to your question while you're there.