Measurement units have historically been defined as quantities (i.e., specific properties) of objects, such as the mass of a particular piece of metal or the length of a particular rod. While the current International System of Units (SI) Brochure endorses this position, the draft 9th SI Brochure proposes to change it, and instead define measurement units as values of quantities. The reason for this proposed change is not provided, but it does not seem plausible that it is related to the redefinition of the SI units in terms of fundamental constants of nature: the very concept of what a unit is does not depend on the concrete way any given unit is defined. This paper is intended to open a discussion of whether measurement units should be defined as quantities or as quantity values, and provides our rationale for maintaining the definition of units as quantities.