Telephoto Lense For Canon 20D. 100-400, or 70-200?

Hi group

I am looking for a telephoto lens for my Canon 20D. I think a zoom lens
would suit me more than a prime lens, because of the flexibility.

Therefore, I was thinking maybe either the Canon EF 70-200mm f/2.8L IS USM,
or the Canon EF 100-400mm f/4.5-5.6L IS USM.

The 70-200 sounds like a better lense for image quality, AF speed and
obviously the wider aperture. However, the 100-400 wins on having the extra
focal length (although I am unsure if I will get on with the push-pull
operation of the 100-400 lens and the dust issues I have heard comes with
it).

So, I was thinking of maybe getting the 70-200 and if I need the extra focal
length, add a 1.4x converter.

Any advice?