Electrochemical hydrogen compression is seen as a promising alternative to mechanical compression in the context of power-togas plants. It can be carried out either as direct co-compression in a water electrolyzer (WE) or via a separate electrochemical hydrogen compressor (EHC). This study analyzes the specific energy demand of different hydrogen generation and compression pathways using WEs and EHCs, both based on proton exchange membrane (PEM) technology, for pressures up to 1000 bar. The energy demand is systematically investigated as a function of design parameters such as pressure, current density, temperature and membrane thickness and presented in overpotential-specific and gas-crossover dependent shares. The analysis reveals intrinsic differences in the compression behavior of WEs and EHCs. In the EHC, permeated hydrogen is simply re-compressed back to the cathode. In the WE, instead, water has to be split again to compensate for the hydrogen loss, causing energetic disadvantages with increasing hydrogen pressure. Moreover, using an EHC enables design parameters to be optimized separately regarding hydrogen generation and compression. Therefore, at low current densities, compression via EHC is already favorable to co-compression via WE for pressures above 4 bar. With increasing current density, however, this intersection point shifts up to pressures above 200 bar.