My main concerns with the sigma is it seems to have weak border performance on the photozone charts,
Look at Photozone's sample pictures. Do those images look bad to you? If you are using this on a crop camera (as I do), then there's even less to worry about.
It is heavy, and if you are thinking about handholding it all day, you might not want this one. It's 6.5 pounds (or so) and feels like it. It's about double the 70-200mm IS II's weight.
quality control issues.
You either get a bad copy, or you don't. If you get a bad copy, return it. That's it. The stories I've heard about 120-300mm OS lenses shipping with dead or damaged focus motors were easily determined from the start. Mine had no problem. What exactly do you want us to tell you here?
With the Canon I am concerned about image quality loss with the extenders and of course losing the 2.8. With a 1.4x extender it is about $450 cheaper than the sigma though.
You lose IQ with either lens and a TC. With the Sigma 120-300mm and an EF Extender 2X III, there is noticeable quality loss, but wide open the lens still seems to perform better than the Sigma 120-400mm OS APO (a fairly recent design) ever will. I can't make a comparison to the 100-400mm L.
You said a 300 mm prime is out of your budget, but an f 2.8 lens with a 1.4 extender will have the same aperture as Canon's much lower cost f4 300mm L prime (and won't be as sharp.) With a 2x converter, it becomes a 5.6, which is the same as the Canon 100-400 L zoom (which is also less expensive).
You can't make this comparison the way you want to, either. In the case of Sigma, I found the 120-300mm with a TC still outperformed the 120-400mm. For Canon, it's not clear that the 100-400mm is as bad a performer as the Sigma 120-400mm, but the zoom may similarly leapfrog the performance of the older lens with a TC (there are some comparisons out there that should give a decent idea either way).
I can't stress enough how helpful f/2.8 is when you need it and you can do without a TC, either at 200mm or 300mm.
If you don't need a zoom, then the Canon f4 is the cheapest, fastest option.
Undoubtedly true, but you can't turn the 100-400mm into a 600mm equivalent lens while retaining AF (ignoring for a moment that many people have said the 120-300mm OS's 300mm length is something more on the order of 280mm or so; it's well above 540mm at the shortest).