I had the Sigmonster for a long time, and now use the 500 f4 IS and 400 2.8 IS for birding. The sharpness of the Sigmonster compares well with the 500 f4. The 500 is faster focusing, but the Sigmonster's HSM is no slouch and can catch BIFs too. At fast shutter speeds, I turn off IS anyway so the Sigmonster has no disadvantage here.
If I have to shoot motorsports or surfing (or other outdoor sports in daylight), I'd opt for the Sigmonster over the 500 f4/400 f2.8 mainly because of framing flexibility. Adding/removing TCs from the big whites takes too long a time, and that can result into lost decisive moments. A quick twist of the Sigmonster's zoom ring can optimize composition in a split second.
That said, I'd opt for the 500 f4 IS for general birding because of IS, portability and weather sealing.