An energy systems comparison of grid-electricity derived liquid hydrogen (LH2) and liquid ammonia (LNH3) is conducted to assess their relative potential in a low-carbon future. Under various voyage weather conditions, their performance is analysed for use in cargo transport, energy vectors for low-carbon electricity transport, and fuel supply. The analysis relies on literature projections for technological development and grid decarbonisation towards 2050. Various voyages are investigated from regions such as North America (NA), Europe (E), and Latin America (LA), to regions projected to have a higher electricity and fuel grid carbon intensity (CI) (i.e., Asia Pacific, Africa, the Middle-East, and the CIS). In terms of reducing the CI of electricity and fuel at the destination port, use of LH2 is predicted to be favourable relative to LNH3, whereas LNH3 is favourable for low-carbon transport of cargo. As targeted by the International Maritime Organisation, journeys of LNH3 cargo ships originating in NA, E, and LA achieve a reduction in volumetric energy efficiency design index (kg-CO2/m3-km) of at least 70% relative to 2008 levels. The same targets can be met globally if LH2 is supplied to high CI regions for production of LNH3 for cargo transport. A future shipping system thus benefits from the use of both LH2 and LNH3 for different functions. However, there are additional challenges associated with the use of LH2. Relative to LNH3, 1.6 to 1.7 times the number of LH2 ships are required to deliver the same energy. Even when reliquefaction is employed, their success is reliant on the avoidance of rough sea states (i.e., Beaufort Numbers >= 6) where fuel depletion rates during a voyage are impractical.