Many people have a hard time choosing between these options, including myself. These lenses are so expensive, that you have to view them like the long term investment that they are.
I like to shoot Sports, Surfing, BIF, Motorsports, and Airshows. I'm not familar with the sigmonster at all. As far as the the Canon super-telephotos. They will all produce exceptional results and are in the top of their class. So, the choice does come down to what your focal range requirements are.
I have the 300mm f/2.8L IS, 1.4X and 2X extender, 7D, MKIV and 1DX. I have also tried the 400mm f/2.8L IS version I.
Focal length requirements willl come down to Camera body FF vs crop factor and with or without extenders. The 1.4X reduces AF speed by approx 50% and the 2X reduces AF speed by about 75% according to Canon. The AF speeds of these lenses are already very fast, so half as fast, is still pretty fast.
As you are aware the degradation with the 1.4X is mild and acceptable, however the 2X is more so. It's always best to buy the FL that you need the most and just use the extenders as a bonus.
I use the 300mm f/2.8L with the MKIV (1.3 crop) for 390mm and many times I add the 1.4X for 546mm which gets to be a little too long for sports, but is good for BIF.
I do think that the 500mm would be fine for field sports though. A lot of sports shooters use the 400mm with MKIV for 520mm. With the exceptional ISO's of the 5DIII and 1DX, I think that the 500mm f/4 will become more popular for sports, unless someone shoots a lot of night games and really needs f/2.8.
If you add the 1.4X to the 500mm, then you have a nice light-weight 700mm f/5.6 BIF and wildlife lens. If you shoot smaller birds from far away then you'll need the 600mm and then you can add the 1.4X for 840mm. But I think the 600mm is too long for sports. Sure you can get the exceptional isolation portrait shot, but it's a bit too long for general use.
The 200-400mm f/4L +1.4X intrigues me for it's versatility.
Since I already have the 300mm + 1.4X @420mm f/4 for sports, I feel that the 500mm f/4L would be too close to my 420mm f/4 combo. So, I'm considering the 600mm. If I sold the 300mm f/2.8 then I would also consider adding the 200-400mm +1.4X.
Wouldn't this be a killer kit; 70-200mm f/2.8L IS II, 200-400mm f/4L IS+1.4X @560, 600mm with and without 1.4X for 840mm
If I were you I would strongly consider the 200-400mm if 560mm is long enough for you, otherwise the 500mm +1.4X @700mm would provide longer reach. The 500mm will still be very good for sports on full frame, as well as wildlife with the 1.4X, and it's lighter and cheaper.
It's a tough decision, so don't rush it.