I've owned all 3 lenses.
The 70-200mm f4 is great - but I replaced it with the 70-200 2.8, partly for the extra stop but mostly for the IS
, which is Canon's best implementation yet - good for 3 stops in my experience.
The 100-400 is also a great lens, and for aircraft photography, extremely versatile.
Having both the 70-200 & 100-400 plus the 1.4 & 2x convertors, there was a certain amount of redundancy. After careful comparisons, I determined that the 70-200 +2x convertor was slightly inferior to the 100-400 at 400mm. However at other focal lengths, the 70-200 is better than the 100-400 and with the 1.4x convertor it is at least as good as the 100-400 at 280mm.
In the end I sold the 100-400, but it was a difficult call - I should also point out that I have 2 bodies meaning the range of the 100-400 is no longer such a big factor for me.
A small point of correction to dazultra's note: the 1.4x convertor adds 1 stop to the effective aperture, making the 70-200f2.8 a 98-280 f4; the 2x convertor adds 2 stops making the lens a 140-400 f5.6. This is about 1/2 stop slower than the 100-400, however the 70-200's IS
is better than the 100-400's. It is arguably better ergonomically as well, being a ring zoom instead of push-pull.
Colin K. Work, Pixstel