What is the difference between Claims based authentication vs What is provided by OAuth.
I am looking for conceptual difference and not technical difference. When do
Claims-based identity is a way of decoupling your application code from the specifics of identity protocols (such as SAML, Kerberos, WS-Security, etc). It is not only for web applications and is implemented as a .NET library / framework called WIF.
OAuth is a specific protocol by which one web site can obtain user consent to access their private data on another web site.
It is not really the case that you would choose one or the other, in fact they are complementary. Potentially you could use both at once, if you were building a .NET web app that performed OAuth via the WIF.