1) The obvious difference in both lenses - the Tamron lens had 100mm more in its focal length, for wildlife photography, it is important to have as much as possible.
2) The Tamron lens is a bigger and heavier lens
3) The Tamron lens is very much sharper than the Sigma at 500mm.
4) Both have very good image stabilizing system.
5) The Sigma is significantly cheaper than the Tamron.
6) The Tamron is newer.
As to which one is the better lens for you, only you can answer that question yourself.