We investigate whether offshore hydrogen plants are advantageous for the German energy system compared to offshore power plants. Offshore hydrogen could offer a lower levelized cost of hydrogen (LCOH) than alternative hydrogen supply routes and relieve possible bottlenecks in the electricity grid. However, building offshore hydrogen plants would result in fewer offshore power plants that supply valuable electricity with high full load hours to the energy system. Using an optimization model of the German energy system, we investigate the conditions under which offshore hydrogen plants offer a higher value to the energy system. This is done by varying the LCOH of offshore hydrogen and by limiting the maximum capacity of the electricity grid between the coast and inland. The results show that offshore hydrogen is not advantageous if there is no bottleneck in the electricity grid or if it does not yield lower LCOH than onshore hydrogen. However, if both conditions are met, we find between 0.85 GW and 7.91 GW of offshore hydrogen plants for maximum grid capacities between 20 and 30 GW.