Hydrogen produced in a polymer electrolyte membrane (PEM) electrolyzer must be stored under high pressure. It is discussed whether the gas should be compressed in subsequent gas compressors or by the electrolyzer. While gas compressor stages can be reduced in the case of electrochemical compression, safety problems arise for thin membranes due to the undesired permeation of hydrogen across the membrane to the oxygen side, forming an explosive gas. In this study, a PEM system is modeled to evaluate the membrane-specific total system efficiency. The optimum efficiency is given depending on the external heat requirement, permeation, cell pressure, current density, and membrane thickness. It shows that the heat requirement and hydrogen permeation dominate the maximum efficiency below 1.6 V, while, above, the cell polarization is decisive. In addition, a pressure-optimized cell operation is introduced by which the optimum cathode pressure is set as a function of current density and membrane thickness. This approach indicates that thin membranes do not provide increased safety issues compared to thick membranes. However, operating an N212-based system instead of an N117-based one can generate twice the amount of hydrogen at the same system efficiency while only one compressor stage must be added.