The enzyme FeFe-hydrogenase catalyzes H2 evolution and oxidation at an active site that consists of a [4Fe-4S] cluster bridged to a [Fe2(CO)3(CN)2(azadithiolate)] subsite. Previous investigations of its mechanism were mostly conducted on a few "prototypical" FeFe-hydrogenases, such as that from Chlamydomonas reinhardtii(Cr HydA1), but atypical hydrogenases have recently been characterized in an effort to explore the diversity of this class of enzymes. We aim at understanding why prototypical hydrogenases are active in either direction of the reaction in response to a small deviation from equilibrium, whereas the homologous enzyme from Thermoanaerobacter mathranii (Tam HydS) shows activity only under conditions of very high driving force, a behavior that was referred to as "irreversible catalysis". We follow up on previous spectroscopic studies and recent developments in the kinetic modeling of bidirectional reactions to investigate and compare the catalytic cycles of Cr HydA1 and Tam HydS under conditions of direct electron transfer with an electrode. We compare the hypothetical catalytic cycles described in the literature, and we show that the observed changes in catalytic activity as a function of potential, pH, and H2 concentration can be explained with the assumption that the same catalytic mechanism applies. This helps us identify which variations in properties of the catalytic intermediates give rise to the distinct "reversible" or "irreversible" catalytic behaviors.