The aim of this paper is to compare an optimal and a sub-optimal strategy for the Fuel Cell Hybrid Power Systems based on Maximum Power Point tracking algorithms (with global feature or not) with the basic energy management strategy, namely the static Feed-Forward strategy considered as reference. The fuel economy is used as the unique performance indicator. The gaps in fuel economy for two Real-Time Optimization strategies based on Global Extremum Seeking algorithm and Perturb & Observe algorithm are compared to highlight the advantages of the global optimization strategies. Up to 5 L fuel economy was obtained for optimal strategies compared to sub-optimal ones. Also, the gaps in fuel economy are estimated for the proposed strategies using two levels of the FC current slope. The results of this study obtained for constant load are validated on a variable and unknown profile of the load power as well.