We perform a systematic comparison of SAT and CSP models for a challenging combinatorial problem, quasigroup completion (QCP). Our empirical results clearly indicate the superiority of the 3D SAT encoding, with various solvers, over other SAT and CSP models. We propose a partial explanation of the observed performance. Analytically, we focus on the relative conciseness of the 3D model and the pruning power of unit propagation. Empirically, the focus is on the role of the unit-propagation heuristic of the best performing solver, Satz, which proves crucial to its success, and results in a significant improvement in scalability when imported into the CSP solvers. Our results strongly suggest that SAT encodings of permutation problems may well prove quite competitive in other domains, in particular when compared with the currently preferred channeling CSP models.