I tested Tamron 200/500 a couple of weeks ago (I was going to use it for shots of planes and nature) and I refused from my idea to buy it. I got colour aberrations near borders and images went to yellow.
I didn’t try Sigma 170/500 but I know it’s better for nature (goes to green a bit and even adds colours more then in reality). I tested other Sigma lenses a time ago and noticed they all have such traits.
After all I bought a teleconverter for my Nikon 70-300. I lost lens speed of course but got extra zoom for any case. :D
I have the Sigma lens and I think it’s pretty decent.
Obviously there is something of a trade off considering the price, but for the relative cheapness it works well.
If you like photographing wildlife you need something in this range and I reckon you should get either of those lenses because they give you so many more opportunities, particularly for birds.
I think the Tamron lens is more expensive so that put me off a little. I do believe it performs a little better in those tests that the reviews sites do, but perhaps not better enough to justify the price.