There are three families of mononuclear molybdenum enzymes that catalyze oxygen atom transfer (OAT) reactions, named after a typical example from each family, viz., dimethyl sulfoxide reductase (DMSOR), sulfite oxidase (SO), and xanthine oxidase (XO). These families differ in the construction of their active sites, with two molybdopterin groups in the DMSOR family, two oxy groups in the SO family, and a sulfido group in the XO family. We have employed density functional theory calculations on cluster models of the active sites to understand the selection of molybdenum ligands in the three enzyme families. Our calculations show that the DMSOR active site has a much stronger oxidative power than the other two sites, owing to the extra molybdopterin ligand. However, the active sites do not seem to have been constructed to make the OAT reaction as exergonic as possible, but instead to keep the reaction free energy close to zero (to avoid excessive loss of energy), thereby making the reoxidation (SO and XO) or rereduction of the active sites (DMSOR) after the OAT reaction facile. We also show that active-site models of the three enzyme families can all catalyze the reduction of DMSO and that the DMSOR model does not give the lowest activation barrier. Likewise, all three models can catalyze the oxidation of sulfite, provided that the Coulombic repulsion between the substrate and the enzyme model can be overcome, but for this harder reaction, the SO model gives the lowest activation barrier, although the differences are not large. However, only the XO model can catalyze the oxidation of xanthine, owing to its sulfido ligand.