Aircraft manufacturers are currently developing concepts to bring a hydrogen-powered aircraft to market by 2035. One option to realize this goal is a fuel cell based system, which enables emission-free and efficient flying. In contrast to a conventional aircraft that employs a gas turbine as its primary power source, the heat generated in the fuel cell must be actively rejected into the surrounding environment in order to maintain functioning. In this paper, the potential of two-phase cooling for fuel cell systems in aircraft is compared to liquid cooling systems for a 100 kW-stack. For this purpose, Modelica-based simulations are performed to analyze the operation and function of the proposed cooling systems. Two-phase cooling can greatly improve performance by achieving higher heat transfer coefficients and enthalpies of vaporization. Results indicate that two-phase cooling systems can reduce the required pump power by more than 98 %, and a novel bypass architecture offers further benefits in this regard. Additionally, the two-phase cooling systems can decrease the air volume flow rate needed to dissipate heat to the environment by 36 %, leading to a reduction in drag on the aircraft. The temperature difference between the fluid and the membrane can be reduced to less than 1 K, resulting in a more homogeneous temperature distribution in the fuel cell. Further research is necessary to establish the conditions under which two-phase cooling systems can operate stably without exceeding the maximum membrane temperature.