  We compare two approaches to the study of Galois module structures: on the
one hand factor equivalence, a technique that has been used by Fr\"ohlich and
others to investigate the Galois module structure of rings of integers of
number fields and of their unit groups, and on the other hand regulator
constants, a set of invariants attached to integral group representations by
Dokchitser and Dokchitser, and used by the author, among others, to study
Galois module structures. We show that the two approaches are in fact closely
related, and interpret results arising from these two approaches in terms of
each other. We also use this comparison to derive a factorisability result on
higher $K$-groups of rings of integers, which is a direct analogue of a theorem
of de Smit on $S$-units.
