The conceptual importance of the dimensions versus categories question hinges upon a particular philosophical approach to the classification enterprise. Simply put, the question matters only if one is a realist. There are varieties of realism, but all realists share a belief in the ability of theories to represent the structure of reality accurately, or, as some would prefer, with verisimilitude (truth-likeness). Taxonomies too should reflect reality to the extent that taxonomies are theory-laden. A taxonomy is simply a theory's way of slicing up reality.
Theories are unavoidable. Even simple observation is infected by one's theory of optics (Feyerabend). Because observations (and classifications) are theory-laden, pure induction, as a psychological method starting with theory-neutral facts and culminating in full-blown theory, is impossible. What one sees of the world is determined by one's theory. Even popular aphorisms confirm this, as when it is said that one typically sees the glass as half full or half empty, the weather as partly sunny or partly cloudy. What one sees depends upon one's way of seeing, upon one's innate conceptual scheme according to Kant, upon one's freely chosen conceptual framework according to Popper and other critical realists.