I cant speak for digital picture but I can tell you the 70-200 with the 2x was sharper than the 100-400 wide open and that was with two different copies I tried before returning it. The AF speed and ability to lock on birds in flight was not up to it as well.
I worked with both the 100-400 as well as the 70-200 2.8L II with 1.4 and 2xIII TC. I did not have a 1D version body so found the 100-400 AF to hunt a lot due to f5.6 at 400mm and excessive coma wide open. Still, with the 70-200 and 2xIII TC, the AF hunting was less and faster likely due to the increased contrast at f2.8(5.6) having better optics and more contrast for the AF to work with. The TC does soften ever so slightly the image from the 70-200 but it's far better than the 100-400 wide open.
I've just had a look at the digital picture ISO 12233 100% crops and have to disagree with you.
On axis the 100-400L wide open @400 is sharper than the 70-200/2.8 II @200 wide open with either the 2XTC II or the III version!
Never a good idea to put a 2xTC on any zoom and expect brilliant results!
By the way an new version of the 100-400L is due sometime - should be a great lens.