So i'ts for Full frame, the 5D III
Can you tell me the overall image quality of the Sigma 85mm f1.4 vs Canon 135mm f2.0
(resolution, CAs, focusing..etc)
I own both, and the only reason to prefer one over the other would be focal length.
To your questions -- the 135L is a speed demon when it comes to focusing, especially as it has a focus limiter. The Sigma is reasonably fast but not as fast as the 135L.
I've been pretty happy with the overall image quality of both of them, I'd refer you to pixel peeper websites, especially thedigitalpicture.com for more insight here.
I think generally the longer lens will have an advantage in terms of corner sharpness, but the shorter lens has the advantage that you are likely to be able to use it at low ISOs (you can shoot it at 1/85s instead of 1/135s and it is a stop faster).
EDIT: since you're shooting full frame, one thing I'd add to this -- the Sigma 85mm, and the Canon 85mm (both of them) have relatively long MFDs (and therefore relatively small maximum magnification). I doubt this would be a problem on APS-C (where your view is cropped) but on FF I notice it. The 135L has higher maximum magnification (it focuses at similar distance to the 85s), so you can get really tight shots with it.