Yes the 5d III is not a sports camera due to its lower FPS but its focus system has been derived from the 1Dx so there is no doubt that it can be used for sports.
You have mistaken between the D3 and the D3s ...
the D3s is in a different league altogether but like u said different situations need different cameras and for me the D3s is the low ISO king. 25,000 iOS low light wedding reception no problem at all. And D800 for portraits OMG the details it's captures and the ability to retain shadows is amazing!
But in my daily use, I use my 5D mark III as it feels the best in my hands 
btw bro are u in UK? I have a few lens for canon which u might be interested in , lets me know if u finding good lens