It is an interesting proposition.
Love the Canon 300mm F/2.8 IS II, and found the 100-400 marginal. I did find when using either the 1.4 of 2 III teleconverters I really noticed the built in delay in AF / Shooting.
So the question almost becomes if the Canon 100-400 is f/4-5.6 and adding a 1.4 makes it a F/5.6 - 6.3 and 140-560, the resolution seems similar, the Canon probably sharper, but also a built in delay of 40% in shooting.
That can be a significant delay in trying to capture a moment. I also noticed a delay in burst
Now the 200-400 looks like an absolutely sweet lens, one I covet, but at the price?
Obviously the 300, 400 and 600s are going to be sharper lenses.
I have really debated the Tamron as a fill in lens. Images look decent but not superb, but for a lot of things that extra reach can be nice.
The Sigma I expect to be 20% maybe 30% higher, and if it is sharper, may be one I bite on. Not nearly as good at the Canons, but the trade off is perhaps the Sigma, the 7D MKII and some extra compared to what the Canon offering is going to cost way more... To get close, have to sacrifice IS
And more I look at it, I can upgrade my backup 5D MKII to the 5D MKIV, buy the 7D MK II and the new Bigma for probably the same amount as a used 600 MM f/4 IS, and still have cash left.
Canon lens hands down better, but two new bodies and long lens which is decent but not great is a fairly nice compromise
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.