How does http://auth0.com's authentication features compare to Firebase's authentication?
Does Auth0.com, on the Free or Silver plan, provide any authentication features that Firebase does not provide?
One major difference between the two (not mentioned in the blog linked in Jake's answer) is pricing. Auth0's pricing increases pretty quick along with the number of active users (source) whereas Firebase Auth is free to use; you only pay for optional features like SMS, and database usage in case you need to store additional user metadata.
See this question for more about Firebase Auth pricing.