"As developers using Google Data APIs, one of the first challenges is learning and sorting through Google Data authentication schemes: AuthSub, OAuth, ClientLogin, OpenID+OAuth, and so on. Perhaps you may be developing Google App Engine web app and want access to a user's Google Calendar. If you're familiar with Google Data APIs you likely know there're many authentication options available depending on API. So how do you decide? The best place to start is Getting Started with Account Authorization guide. Also, Authentication in Google Data Protocol page provides detail on various authentication methods," explains Google.
Also, refer to following link that provides references to many existing resources and some additional things to consider to help you decide which authentication method to use for your app.
More Info: Google Data Authentication Choices