In practice, the IQ difference between the 100-400mm and the 70-200 II + 2x is probably not going to be too noticeable (or not at all) in real-world shooting. But also, as you mention, using an extender slows down AF - in fact, with the 2x extender there's a 50% reduction in AF speed. That means the 100-400mm will focus faster than the 70-200 II + 2xIII (it's noticable in real-world use, but it's not too bad). Finally, there's cost - the 100-400mm is over $1000 less than the 70-200 II + 2xIII.
Minor nitpick: I'm pretty sure the reduction in AF speed compared to a bare lens is 50% for the 1.4x TC and 75% for the 2x TC.
Yep, found the reference - Here's a quote from the EF 1.4x III review @ thedigitalpicture.com (http://www.the-digital-picture.com/Reviews/Canon-Extender-EF-1.4x-III-Review.aspx
):According to Chuck Westfall (Canon USA): "As with previous EF Extenders, usage of Series III EF Extenders lowers AF drive speed to improve AF performance. When Extender EF 1.4X III is used, AF drive speed is reduced by 50%. When Extender EF 2X III is used, AF drive speed is reduced by 75%. This may seem like a drawback, but in reality subject tracking performance remains quite high when Series III Extenders are used with IS II lenses. This is due to improvements in AF precision made possible by the new microcomputer in the extenders."
And further in the review:Note that "AF precision remains the same as the Series II Extenders when the Series III Extenders are used with earlier extender-compatible EF lenses." [Canon]
Just to clarify, the 70-200 f/2.8L IS II does not benefit from the AF precision improvements of the new III series TC's (Chuck's IS II reference is specific to the new super-tele primes); I believe development of the 70-200 was too far ahead of the new super-teles/TC's to take advantage of the improvements.
In my personal experience, the difference in AF speed between the bare 70-200 IS II and the lens plus 1.4x III is noticeable, but the AF speed of bare lens is so incredibly fast that, in practice, even a 50% reduction to AF speed is rarely an issue (assuming I'm not limited by available light).