The Canon 100-400 won't work with a 1.4x or 2x TC.
I also have both the EF 300/4IS and EF 400/5.6 as well. I use the EF300/4IS with a 1.4x TC, my wife uses the EF400/5.6 most of the time. AF speed is _very_ good with the EF400/5.6L and EF300/4IS + 1.4x TC is pretty good.
I have a Sigma 70-200/2.8, and with a 2x TC, the AF speed is rather slow for birding, my 50-500 is faster.
I miss the flexibility of the 50-500 sometimes, but the AF speed is a good trade-off. If I'm out and about doing more general shooting, then I still occasionally grab the 50-500.