Maybe late to give you any help, but I have both the 300mm f2.8 and 400mm DO (I have got a sharp one).
Both Handle Tc's well. I have performed software calibration on them on a 1DXmk2 the software says the 300mm is as sharper of the 2, and with the 1.4 mk3 (both 1.4 and 2xtc mk3's are sharper then mk2's tcs according to the software) its almost as sharp as the 400mm f4.
The 300mm is sharper at 600mm (2xtc) then the 400mm DO at 560mm (1.4tc) but not that you notice it much in image iq wit the naked eye. There both still quick to auto focus too. But the weight of the 600mm combo is much heavier, can be hand held for very short durations. But the 400mm DO plus tc is very hand holdable. I have done days of show jumping and Motorsport without monopod.
the 400mm at 800mm is still useably sharp, and auto focus is accurate for station or slow moving subjects, bu forget birds in flight.
now that's my lenses like said theres mixed reports on the 400mm DO mk1, where's everyone raves about the the 300 f2.8 is as being the best lens ever. a good copy of either will be better then your 100-400.
Everything here is the 300mm f2.8 plus 1.4tc
https://flic.kr/s/aHsmHneLxK
Everything here is the 400mm DO with and without the extenders check the images and exits see if you tell the differences.
https://flic.kr/s/aHsmGMMJDu
Personally I can, the 300mm f2.8 is has more natural colour imho.
Or 2 simular shots both with the 1.4tc.
_G0I1334 by
Darren Russell, on Flickr
_G0I0463 by
Darren Russell, on Flickr
so ones hand held at 560mm the other 420mm on a monopod with a gimbal head.
this 400mm DO handheld for several hours.
_G0I8362 by
Darren Russell, on Flickr
I hope this helps.