I don't know about the teleconverter, not having used one with either lens. However, I looked at both these lenses last year, to use on my 7D as a replacement for a 70-200 f4 IS. After renting, I chose the 70-300L. I much preferred the size and format (it's a good bit smaller and lighter than the 100-400), I found the IS system on the 70-300L to be outstanding, and yes, I liked the focusing ring better than the push pull mechanism (although this latter is personal preference only; I have a friend who prefers the push-pull). In terms of sharpness, I didn't pixel-peep, but I had a slight preference for the images from the 70-300L; they seemed clearer somehow.
As an aside, I got the 70-300L because I didn't much like using a teleconverter with my 70-200. Teleconverters do affect focusing speed and image quality; the effect wasn't huge with the 70-200, but it was noticeable. I would imagine it would be more noticeable with the 70-300. If you think you're going to need a teleconverter on a regular basis, I'd suggest buying a lens with the reach you need instead.