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The need to reduce emissions from shipping is urgent. Potential future fuel candidates include hydrogen and methanol. This study has attempted to draw a fair comparison between these two fuel types by adopting a bottom-up approach to quantify fuel consumption and emissions. A 10,755 nm voyage undertaken by an LNG carrier was used as a case study. Models were developed for a hydrogen fuel cell energy system and a reformed methanol fuel cell energy system. Simulations calculated the fuel requirements and tailpipe emissions for each option. However, as neither hydrogen nor methanol is naturally occurring, the energy required to produce these fuels should also be considered. Three production methods have been modelled: wind turbines with electrolysis; grid supply with electrolysis; steam methane reforming. Thereafter, the total lifecycle emissions for each fuel option have been calculated and compared to the existing vessel. Typically, this is referred to as well-to-wake emissions, but for green fuels wind-farm-to-wake may be more appropriate. Results showed that switching to methanol reduced tailpipe emissions by a maximum of 8.3% and wind-farm-to-wake emissions by 18.8% but only if the fuel can be produced entirely from renewable energy. A liquid hydrogen fuel cell energy system produced zero wind-farm-to-wake emissions and required 33.3% less renewable energy than methanol.