I have just purchased a TC17E II for use with my 70-200 f2.8 lens a few weeks ago. I was previously using a Sigma 100-300 f4 with Sigma x1.4 TC (both now for sale!).
Unfortunately, I have not yet tried the TC with my 70-200 lens! I really must try get out with it! If I do find the time to get out with it soon, i will post and let you know how it is.
I did try a friends TC20e III (on my 70-200 f2.8) and it seemed fine, but I wanted a slightly faster lens and having read up a lot decided to go with the TC17 as a compromise. I couldn't justify buying a new lens for the few occasions that I need the extra reach, much as I'd like to, so common sense (and bank manager) kicked in.
My partner uses a Kenko PRO300 1.4 TC with her Canon 70-200 f4 and it seems to produce reasonable results. She has a canon x2 TC but it does not autofocus with her f4 lens unless it is via live view (which does work remarkably well if a little slow). The Kenko also allows her to use it with her Tamron 150-600 lens, again using live view to autofocus. So I wouldn't rule out a Kenko TC.