I have been considering the merits of these two lenses for quite some time, considering that I need a Supertele.
Just some thoughts from my perspective.
When the 400 f/4 DO ll came out, I recall reading it was sharpest wide open and gradually decreased in image quality upon stopping down.
The 300 f/2.8 IS ll seems to increase sharpness upon stopping down-until f/11, anyways.
When the comparison of the 2 lenses were done @ lensrental.com, it was said that the 400 DO ll was sharper wide open than the 300 2.8 ll @ 2.8 and @ 420 f/4, and I agree w/that. I think it's important to look beyond that and see if that changes upon stopping down, especially w/teleconverters applied.
At the Digital Picture, it seems-to me anyway- the 300 2.8 ll w/1.4 converter get better than the 400 f/4 DO ll natively @ f/8 and f/11.
The 300 2.8 ll w/2.0 converter seems slightly better, overall, than the 400 DO ll and 1.4 converter @ f/8 and f/11. The contrast appears better on the 300 2.8 ll than the 400-even though contrast can be corrected. Some comparisons seem close or even, but the 300 looks slightly better overall.
As some posters have mentioned, 300 native, 420 and 600 seem like good focal length options. Better than native 400 and 560 f/5.6 for those of us w/out f/8 bodies.(Yes, that's subjective)
The 400 DO ll seems to be a great and practical lens considering its weight.
For me, I think the 300 w/1.4 and 2.0 converters win because of contrast, sharpness, aperture, 400 DO ll onions, and price. The 300 f/2.8 w both teleconverters is cheaper than the 400 DO ll @ Canon price watch.
$4,999.99 US vs $6449.00 US. That helps make my decision much easier.