Was also considering between the two a few months ago. Things to consider are cost, weight and most importanly use cases. If use case is for lower light and fast speed lens then you have little choice. If cost is a consideration that likely you should consider the 70-300 instead as it is value for money for the $600+ cost.
Have bought the 70-300mm finally after all the above considerations as I have the kit 18-135mm lens already. (else would have considered the 18-200mm overpriced lens instead.)
Anyway the 70-300 mm VR is quite good for the $$$. Took some picutures at 300mm and they were still clear at 100%. Surely not the $600+ lens level of quality. Cannon will cost $200+ more for the same lens and that lens is not as good and less build quality to me.
If you like going to the zoo and bright events vs dark events than the 70-300 should be enough.
Brokeh for the Sigma f2.8 will be much better vs the 70-300mm for sure as well as catching F1 night race would be an advantage. But still think VR is needed with the f2.8 lens. (If only Sigma has some type of VR/IS built-in.)
Anyway will consider a f2.8 that has VR/IS/OS etc only for that price of over $1.5K lens. Else think it is a little under capable. (Do not have strong stable hands).
Anyway have fun deciding. Else buy a 2nd hand 70-300mm when someone upgrades. Or just but the 70-300mm first like me.