The 100-400 wide open at 400 suffers from some coma which affects a camera's ability to phase detect focus. I found that the 100-400 hunted more for focus than a 300 with 1.4xiii.... even more than the 70-200 with a 2xiii.
If I were making a purchase decision, the 100-400 would be at the bottom of my list (if cost was not a major driving issue). All things aside, a used 300mm F2.8L IS (old version) with a 1.4xiii is the best "low" cost choice and still get tack sharp images wide open.
300mm F/4L or 400mm F5.6L would be my next choice.
LOL Lets see all and all I prefer the Canon 1Dx to the 5D MKII
That is pretty much your comparison almost. 300MM F/2.8 IS (1st version) is a $6500 lens ($12K retail)
I am assuming the new Bigma will be more like the Tamron, but better build all and all, so expecting more $1500 or so.
Part of the attraction with a Telephoto zoom is range. I have used the 300mm /f2.8 IS. Loved it. At the same time though, hated it as well when shooting sports because often I only had a small field to shoot in, where as having a range, I could continuously shoot action coming towards me and get a dozen shots of an approaching athlete over a few seconds versus a smaller segment of time.
No doubt a 5.6 - 6.3 is limited, but a fair amount of the time when I was shooting the 300MM I was shooting at 5.6 - 8 anyways
This will not be a nighttime or overcast lens, but for daylight, very serviceable.
As well... there is also 200mm of reach more.
Other part of performance... Again... AF.... When using the teleconverters either 1.4 or 2 the AF is deliberately slowed by that same factor as well.
Having a tack sharp image but just a smidge too late can be useless as well.
Depends on what you are shooting.
For sports and action I want to hit the shutter and CLICK and not wait wait click. Now if Canon introduces a version IV of the Teleconverters where AF not slowed, then that could be a different matter.