Having been through this pain myself, i eventually went with the Sigma C, Reasons why Weight and cost, the differences in the sport are only really noticeable at the long end 600mm, where it does go ahead in the sharpness stakes, quite a lot of reviews talking around this dilemma and the pros and cons at differing MM over each other.
One thing that sigma have is the USB dock, and if used properly with products like Focal pro, you can dial in the lens to be even sharper, The USB dock allows 16 variations over 4 segments at 150mm 250mm 400mm and 600mm for you to dial in the focus if you feel you need more.
The Nikon is a very good lens, the problem i had with it is the 200mm short end on my D500 is effectively 300mm which is massive for what i do, the sigma is slightly shorter ar DX 225-900mm which helps me a lot in shooting motorsports. The other thing is weight, when i walk around the track the D500 and SIgma C do become heavy, but with the sport i bet its a killer, and also the fact that i pan a lot panning with a 3KG lens just wouldn't be doable for long.
For Birding and Wildlife id consider all 3 and probably go for the sport
For Bikes Cars and Birding id go Sigma C or Nikon, but prob Sigma due to the ability to have the USB dock
As for Tamron its as good as the Sigma, i only went sigma because of 2 things You can lock the lens at varying focal lengths and you also have 2 custom switches on the lens, so that once you've attached the USB dock, you can in essence have lightning fast focus on 1 and super duper steady shot on 2 and normal is normal, good for when you want to test things....the other is the Tamron is labelled a dust pump, at least the Sigma C has some sealing and the sport is fully sealed..