Differential forms aren't exactly comparable to GA... I would instead look at the relation between exterior algebra and GA. Differentials are a concept that th

Differential forms aren't exactly comparable to GA... I would instead look at the relation between exterior algebra and GA. Differentials are a concept that the comes from doing calculus on manifolds, and exterior products of differentials are just used for tracking information about oriented volumes. To answer your question (switching differentials forms for for exterior algebras), you wont miss anything, as the wedge product is part of a GA.