This work aims to analyse and compare the thermodynamic performance and size of two types of solid oxide fuel cell (SOFC)-based plants. The former is the conventional H₂-fed plant based on SOFC with an oxygen-ion conducting electrolyte (SOFC-O), and the latter is based on SOFC using a proton-conducting electrolyte (SOFC-H). Thermodynamic analysis reveals that in the SOFC-H system, due to H₂O formation at the cathode side, not only the anode concentration losses decreases, but also the partial pressure difference between H₂ and H₂O increases which leads to an increase in Nernst voltage compared to the SOFC-O system. Due to this, SOFC-H and SOFC-O based plants exhibit different performance in terms of the cell voltage, power, efficiency, stack outlet temperature and size of heat exchangers used for preheating the fuel and air. The results indicate, for current densities less than around 3,000 A/m², the energy and exergy efficiencies of SOFC-H-based system are more than those of the SOFC-O-based plant. This results in reduced area of heat exchangers per unit power used in the SOFC-H-based plant as compared with the SOFC-O-based plant. In addition, the sensitivity analysis demonstrates that using thin cells in the SOFC stack is favourable for the SOFC-H-based plant.