This paper investigates the viability of different fuel cell types in a ship power system, where hydrogen and ammonia are considered as zero-carbon fuels. The identification of alternatives to diesel-powered ships is performed by taking into account the environmental and economic indicators of the considered power systems, determined by Life-Cycle Assessment (LCA) and Life-Cycle Cost Assessment (LCCA), and further compared with the existing diesel power systems of three passenger ships operating in Croatian coastal waters. Special attention is paid to fuel origin, where fossil fuels (grey fuel), fossil fuels followed by CO2 capture (blue fuel), and those produced from renewable energy sources (green fuel) are considered. The results of the research indicate that fuel cell systems with grey hydrogen and grey ammonia are not environmentally friendly, while fuel cell systems with the blue and green types of these fuels have a lower impact on the environment than a diesel-powered ship, with a reduction of up to 84% in CO2-eq emissions when green ammonia is used. Regarding profitability, the diesel-powered ship has the lowest total costs, while the second most cost-effective option is the fuel cell system with blue ammonia as fuel with 27%-43% higher costs than a diesel-powered ship, depending on which type of fuel cell is used. Although blue ammonia is a cheaper fuel than diesel fuel, the lifetime costs of the fuel cell power system are affected by relatively high investment costs (fuel cell, battery, cracker, etc.) and equipment replacement costs.