The maritime sector is undergoing a critical transition driven by increasingly stringent emissions regulations from the International Maritime Organization (IMO) and the European Commission (EC). Among the leading alternative fuels for marine diesel engines, methanol and liquefied natural gas (LNG) have gained significant attention. This review synthesizes recent research and industry data to compare the two fuels across physicochemical properties, combustion performance, emission behavior, safety, and economic feasibility. Methanol, a liquid under ambient conditions, enables easier storage and refueling using existing liquid-fuel infrastructure while providing substantial reductions in sulfur oxides (SOx), nitrogen oxides (NOx), and particulate matter (PM) emissions. However, its low energy density and the formation of formaldehyde remain drawbacks. In contrast, LNG offers higher volumetric energy density and immediate reductions in carbon dioxide (CO₂), SOx, and NOx emissions but requires expensive cryogenic storage systems and faces the persistent challenge of methane slip. Economically, LNG engines entail higher capital investment yet support short-term regulatory compliance, whereas renewable methanol offers a scalable pathway toward long-term carbon neutrality. Overall, the optimal choice between methanol and LNG depends on operational profiles and strategic objectives, with LNG serving as a transitional solution and methanol representing a flexible, future-proof option for sustainable marine propulsion.