Just to clarify....
You lose one stop of light when you use a 1.4X... If your lens is an f2.8, it will effectively behave as an f4 with the 1.4X teleconverter on it.
You lose two stops of light when you use a 2X... The same f2.8 lens will effectively act as an f5.6 with a 2X TC on it. Or, if you put it on an f4 lens, that would act as an f8.
Your old 50D is technically unable to focus with less than f5.6 (and then only the center AF point is supposed to work). Your 1DIII is rated to work with f8, center AF point only. Only the 1D series (and old 1V and EOS-3 film cameras) are rated for f8.
There are some workarounds... some third party teleconverters don't "report" to the camera... it doesn't know the TC is there, so it still tries to focus, and sometimes in good light can do so pretty well. Also, it's possible to tape up a couple of the electronic contacts on a teleconverter to fool the camera into trying to focus.
The less light reaching the AF point array in the camera, the slower it will focus and the more it will struggle to focus. So a 2X teleconverter also might slow focus more than a 1.4X, but both will cost a bit of focus performance, too.
Just think of teleconverters as fancy magnifiers. Higher magnification (2X) means more loss of image quality than lower magnification (1.4X).
Just how much IQ is lost depends upon lens and teleconverter. In general, prime telephotos work better with teleconverters, than zooms do. Canon recommends 135/2 and longer lenses with teleconverters, as well as their 70-200 zooms (the f4 zooms will be limited to 1.4X on most cameras). Particular combinations work better or worse.
With my 70-200/2.8 IS (Mark I), I'll use a Canon 1.4X II on it without much concern... but I won't use a 2X II... there's too much loss of IQ for my tastes. The new 70-200 Mark II and 2X Mark III are a better combo... A lot more people find the images acceptible and usable.
I really don't use the 70-200 + 1.4X much, though... since I have a couple 300mm lenses that I'd rather use since they generally give better results.
I use 1.4X II on EF 300/4 IS a lot more often. I use both 1.4X and 2X II on 300/2.8 and the 1.4X on 500/4. On rare occasions, I've used 2X on the 500mm... IQ is good, but AF dosn't work on a lot of cameras and it's damned hard to get a steady shot with what is effectively a 1000mm lens, even with IS.
There are some good third party teleconverters, too. Most who have used it and compared think the Kenko Pro 300 1.4X rivals the Canon 1.4X TCs for sharpness and image quality. The DG version slows focus more, while the latest DGX version improves on that a bit. Kenko also makes a less expensive 1.4X that doesn't offer as good image quality.