Microsoft does have Azure AD B2C as a solution for CIAM, but for more complicated Customer Identity and Access Management scenarios Microft has no real offering. That’s the reason why you might consider specialized solutions like Auth0 (pronounce Auth Zero). Auth0 exists since 2013 and offers an Identity as a Service Solution (IDAAS) which can be hosted in either a private AWS cloud or the public AWS cloud. Azure will be supported as well in the near future.
Feature wise there are little or no differences between Azure AD B2C and Auth0. A key diffentator might be that Azure AD B2C is more inclined towards Azure-centric organizations. For feature updates and roadmap, Azure AD B2C might also be preferred. It’s the specialization on CIAM, that can make the difference in favor of Auth0.
Anyways, make up your mind yourself.
Here’s link to a video on Auth0 that might interest you: Auth0 Demo
Fresh from the press: Last week it was announced that Auth0 has been acquired by Okta.