Hi,
All three types have different usage.
Prompt:In this case users needs to enter the user name and password every time when they are going to refresh the reports. painful for users to enter user name and password every time.
Predefined- user name and password is staticin the connection..Same for all users.In this case SAP BW data authorization will not work. Everytime users will see the data in the report based on the authorization of particular user name which is defined in the connection.
SSO- SSO setup is the one time activity.no prompt for user.BW data authorization will work with SSO authentication.No need of updating the user name and password while moving connections in the different environments.Users only can see the data where they are authorize.
Amit