Off-grid photovoltaic–battery–hydrogen systems are increasingly considered for remote and deployable installations. However, the benefit of a predictive energy management system (EMS) over a simpler rule-based EMS remains unexplored. This paper compares a rule-based EMS and a predictive EMS based on linear programming for a deployable system supplying a 1000-person military camp. A Python-based simulation framework models five years of operation at 15-minute resolution in four regions: Baltic States, Romania, Mali, and Congo. The predictive EMS reduces diesel fuel consumption and CO2 emissions by 5.54% in the Baltic States and by 9.01% in Romania, while only marginal improvements are observed in Mali and Congo. These results show that the benefit of predictive EMS depends strongly on climatic conditions.