I think it all depends on how you define hypervolume. If you say it’s a positive real number constructed by means of integration, then you can certainly compare them across objects of various dimensions. When you say “units” I immediately think of stuff like bivectors and trivectors where you can’t reduce one to another without losing important geometric properties. But here we are talking about just the scalar part which is as “unitless” as can be.
Integration when extrapolated to many dimensions has many nuances, and be careful that you don't have a circular definition of hypervolume in terms of integration.
For a simple example of difficulties consider comparing the volume of two distinct k-unit spheres embedded in R^n where n>k.
