I have the 70-200 F/4 and I had this same problem when trying to decide whether I would get the Sigma or not.
Mine somewhat became decided for me because I found the Canon at a price I couldn't turn away and also I did not want to blow the budget on my first big spend lens. You however are much more experienced than me so I presume this would not be a factor for you.
The 70-200 pros:
- Light and super easy to handle
- The built quality, it just has this presence when you hold it
- The F/4 is quick, ok not 2.8 quick but I am a daytime person so it does not affect me at all
- The sharpness
This is an unsharpened and hardly touched photo, literally just took it and resized it for my web-site:
If you would like to view a 1600 x 1200 version (half the original size) you can view it here-
LINK - Note the rain detail.
I took this at F1 testing with the lens, I applied sharpening after however this was only because I lost some detail when resizing: