I recently discovered Clifford's geometric algebra and its application to differential geometry. Some claim that this conceptual framework subsumes and generalizes the more traditional approach based on differential forms. Is this true?
More generally, are these frameworks strictly equivalent? I have heard that geometric algebra is only a suitable approach once a metric tensor has been chosen. Thus, it would seem that this approach is in fact less powerful.
Putting aside all personal and aesthetics preferences, which framework is more general (if any)?