Due to their great energy efficiency and zero carbon emissions, fuel cell aircraft propulsion systems have become a crucial alternative to conventional fossil fuel-based power in the context of the aviation industry’s increasing attempts to become carbon neutral. This study focused on proton exchange membrane fuel cell (PEMFC) and solid oxide fuel cell (SOFC), systematically analyzing their working principles, system architectures, key technological challenges, and applicable scenarios. The research also compared these systems with lithium battery propulsion systems from multiple perspectives, including energy carrier type, power characteristics, service life, and environmental benefits. The findings reveal that while SOFC have great promise for long-endurance missions, PEMFC are better suited for short-range aircraft applications. Although challenges remain in hydrogen storage, thermal management, system integration, and cost, continued advances in structural optimization and hybrid energy architectures are expected to significantly improve the endurance and emission reduction performance of fuel cell-based aviation power systems. These developments support their role as a critical technological pathway toward green aviation.