The 70-200 f/2.8LII lists for $800 more than the 100-400 ($2,500 vs $1,700), adding a 2xIII extender ($500) puts you $1,300 poorer with the 70-200. Also, when there is a new 100-400, it will likely rival the 70-200 f/2.8II in price.
However, if, for you, the cost is not a problem, and the 201-400mm range is "occasional" use only, the extra two stops of aperture, coupled with outstanding IQ sans extender, and very recent IS/AF systems would suggest the 70-200 f/2.8 II is the lens of choice.
I've been using a 100-400 for about two years, and while I love it for wildlife, there are times I'd rather have had faster AF and/or better IS. The 100-400 is a 15-year-old design, and sometimes, it shows.