We report on a comparative study of the profile of the CKM unitarity triangle, and the resulting CP asymmetries in B decays, in the standard model and in several variants of the minimal supersymmetric standard model (MSSM), characterized by a single phase in the quark flavour mixing matrix. The supersymmetric contributions to the mass differences ΔM_d, ΔM_s and to the CP-violating quantity |ε| are, to an excellent approximation, equal to each other in these theories, allowing for a particularly simple way of implementing the resulting constraints on the elements of V_{CKM} from the present knowledge of these quantities. Incorporating the next-to-leading-order corrections and applying the current direct and indirect constraints on the supersymmetric parameters, we find that the predicted ranges of \sin 2 βin the standard model and in MSSM models are very similar. However, precise measurements at B-factories and hadron machines may be able to distinguish these theories in terms of the other two CP-violating phases αand γ. This is illustrated for some representative values of the supersymmetric contributions in ΔM_d, ΔM_s and |ε|.

30 pages, 9 figures; typos corrected, minor notation change; matches version to appear in the European Physical Journal C