For example 2-categories seem simpler at first compared to double categories because the latter is a "wider environment" (cf Bertozzini), however when doing calculations, many people prefer to use double categories (cf Brown) and when we describe them in the 2-arrows-only language it seems that double categories have less axioms. (Recall the theorem of Brown-Mosa-Spencer that the category of 2-categories is equivalent to the category of edge symmetric double categories with connection and the theorem by Ehresman that all double categories can be embedded in an edge symmetric double category.) It seems that more work has been done on n-categories though, why is that? Is it easier to start with n-categories?