Despite optimizing giant magnetocaloric effect (GMCE) in key material systems (MnFeX, La(Fe,Si)13, NiMnX Heusler alloys), practical GMCE-based magnetic refrigeration is unrealized. One problem is the lack of direct cycle-based performance comparisons between GMCE refrigerants, so that despite much magneto-thermal characterization, it remains unclear which material is optimal for a given application. Further experimental investigations are unfeasible, since performance metrics (e.g., cooling power, % Carnot efficiency) are both material- and cycle-dependent, with additional complications arising from hysteretic path-dependence. Here we present an alternative thermodynamic modeling approach, combining Preisach hysteresis models with experimental data sets to simulate GMCE alloys' state evolution under specified cyclic conditions. Performance metrics are calculated and compared for alloy compositions within each GMCE class undergoing magnetic Ericsson and Brayton cycles between 0 and 1.5 T. Hence for the first time, we directly compare the cycle-dependent performance of GMCE alloys, specifying trends in which are optimal for given applications.