In this study, we compared two different types of propulsion systems for a supersonic unmanned aerial vehicle (UAV) flying at Mach 1.8, which are using two different types of fuel to determine their characteristics and advantages. Also, investigate the effect of various factors such as altitudes and key design parameters of the propulsion system on efficiency and flight duration. These proposed propulsion systems are using a solid oxide fuel cell (SOFC) to generate the heat required for the operation of the turbine and generate thrust. The hydrogen for SOFC is either stored in the tank or generated by the internal reformation of methane inside the fuel cell. We studied the effects of several key design parameters for these engines in different flight conditions and altitudes; carrying out a multi-objective optimization for each proposed propulsion system to maximize the thrust of the engine while keeping the fuel consumption at a minimum rate to achieve the longest flight duration. Then we determined the best conditions where the acceptable thrust is accompanied by reasonable flight duration. Results indicated that the efficiency and generated power of the propulsion system will increase by higher flight altitude or compressor pressure ratio. Also, due to the recirculation of fuel in the SOFC’s anode, we observed higher efficiency in comparison when hydrogen is used; since anode-recirculation causes higher fuel utilization. The optimization result shows that the efficiency and fuel consumption for the hydrogen-fueled system is 48.7% and 0.0024 kg/s, respectively, and 67.9% and 0.0066 kg/s. for the methane-fueled engine.