I figured out quickly when investigating 'big whites' though that using a x2 TC is really not something you want to have to do on any regular basis. Is seems that getting a lens to use primarily with a x2 TC is not a great idea (if not for IQ, then definitely for AF). If I thought I was going to need to use a x2 on the DO a lot, I'd probably suck it up and get a 500 f4 to use with a 1.4. Both size and weight of the DO really appeal to me though - I will be hiking with it.
I have to sound a note of disagreement. I use the 2xiii (and occasionally the 2xii) on the 500LII and it works fine. Not as fast or as sharp as with the 1.4x but still very good (albeit not fast/erratic subjects like BIF). It's worth stopping down from f/8 to f/10 to have optimal sharpness (on the 5DIII at least).
While there is no doubt the X1.4 is preferable if reach isn't needed the X2 III is well worth owning. There are many CR examples. The only time for me that the AF with the 6D was too slow was if focus was lost completely and it had to recover. If a bird is identifiable within the viewfinder it snaps virtually instantly. Not the best for BIF for sure but that's what I used for my pretty acceptable eagle shots this spring on the 1D4 (300 2.8 II X2 III). Loose the bird for a moment and the shot would be lost due to searching, so the trick was to not hit back button focus unless the bird was under the focus point.
One thing that is hard to come to grips with is the reality that IQ keeps climbing with each generation. Take the 7D for example, since it was a very popular birding camera. Should all the 7D shots be canned because the 7D II is significantly better. It's tough if you tend to be a perfectionist and look at the technical details more than the artistic merit. My head says no we should not denigrate shots that are not up to the latest highest technical level and yet there I am focusing on sharpness just like everyone else, I guess.
Think of paintings. Are the only good ones those that have every feature displayed to the utmost degree of sharpness? So what gives?
Well exactly. Many many excellent reference shots of birds on Wikipedia were taken with the original 7D, and most are still top notch - getting close to the subject, a nice creamy background, good light, good pose - these are all as important as sharpness, and none of them rely on having the newest gear (I suppose a faster burst means you have more poses to choose from, but otherwise...)
5D mark III, 50D, 300D, EOS-M; Samyang 14mm f/2.8, 24-105L, 35 f/2 IS, MP-E, 100L macro, 500L IS II, EF-M 18-55; 1.4xIII, 2x III + 2xII extenders; 600EX-RT; EF-M--EF adaptor.
Former lenses include: 70-200L f/4 non-IS, 85L II, 200L 2.8, 400L 5.6