I have a 60D and 580EX II, and I have the same problem (focus takes 2-3 seconds and often misses with AF assist).
Ok, now it's getting really strange - at least with my 60d and the 70-300L & 100L the camera near focuses instantly without hunting with the af assist beams of the 430ex2 and 600rt. It takes just a little longer than in good light because it beams, focuses, beams again and does the final focus. If your 60d hunts then there's definitely something wrong with your setup.
Found the problem (at least in my case). It turns out that my 580EX II has some wiggle room in the hot shoe, and was misaligned for interacting with my selected AF point. I had to turn off all the lights in my room, and look really closely to see the issue. Adjusting the flash a little in the shoe fixed the problem. I wounder if maybe some of the users here are experiencing this same issue?
Try going into a dark room, and focusing on a white wall, you should be able to see if the beam hits in the location of your selected AF point. If not, there is a misalignment with your flash. This could explain why some, but not all, members are seeing the problem on the 5D3.