Claims based authorization VS Role Permission based authorization

Hi All,
Our team has recently implemented a role permission based authorization so that we can have granular control. This is similar to what Rockford Lhotka suggests here http://www.lhotka.net/weblog/PermissionbasedAuthorizationVsRolebasedAuthorization.aspx 
I have also read about the Claims based authorization which to me looks very similar to what we have. Can some one put in simple terms what the advantages of claims based authorization are.


Thanks for your time,
Cheedep

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