Agree with previous posts that the 400 Canon prime is sharper (gets extremely sharp if you close it a bit, to f/7.1 or so). If you use a teleconverter on it though, the sharpness goes away, along with the ability to autofocus (unless your camera can AF at f/8...still isn't worth the trouble though). Why not just wait for the new 100-400? That way you could let everyone know how much disposable income you have! It will be priced in the $2500 range, because of Nikon's new 80-400.
I bought the Sigma 120-400 instead, it works great, costs half the money. Don't regret it at all, rather I see myself keeping it a long time. Very sharp, especially on the 6D, and especially at distances closer than 100 feet. Might not be as sharp as the Canon 100-400, zoomed out to 400mm on an 18mp crop camera (especially at infinity focus)...but then again it might be. Really depends on sample variation. The color rendition via the Sigma, especially at wider than 200mm, is awe-inspiring. It's not just "warmer" either...it's better. The Canon "cool purple" color cast is banished! Contrast of the Sigma at wider than 200mm is very high, so is sharpness...to the corners at f/4.5 on the 6D. Above 200mm some of the contrast and color go away, but then they also go away on the (current) Canon 100-400. The IS on the Canon is slightly better in some instances, but it's not that different. The IS on the new Canon 100-400 would likely make it worth the money, even if sharpness isn't increased by a lot...and it just might be.
While the Sigma does hunt a bit if there is bright contrasty limbs in front of or behind the bird, for the most part it grabs the bird pretty easily. Toward the wide end of the zoom range, it does birds in flight with servo focus on the 6D, almost as well as my 70-200 f/4...which is really saying something. I've not had a chance to try a bird in flight in servo mode closer to the 400mm end yet. I'm sure it would work great if the bird was large and at a distance, and in decent light. Small birds at close distance "in flight" at 400mm, are kind of difficult to keep in the field of view.
Obviously the best zoom lens is the new Canon 200-400 f/4...if money is no object. The new Sigma 120-300 f/2.8 is probably worth a try, too.