Alternative fuels such as hydrogen, compressed natural gas, and liquefied natural gas are considered as feasible energy carriers. Selected positive factors from the EU climate and energy policy on achieving climate neutrality by 2050 highlighted the need for the gradual expansion of the infrastructure for alternative fuel. In this research, continuity equations and the first and second laws of thermodynamics were used to develop a theoretical model to explore the impact of hydrogen and natural gas on both the filling process and the ultimate in-cylinder conditions of a type IV composite cylinder (20 MPa for CNG, 35 MPa and 70 MPa for hydrogen). A composite tank was considered an adiabatic system. Within this study, based on the GERG-2008 equation of state, a thermodynamic model was developed to compare and determine the influence of (i) hydrogen and (ii) natural gas on the selected thermodynamic parameters during the fast-filling process. The obtained results show that the cylinder-filling time, depending on the cylinder capacity, is approximately 36–37% shorter for pure hydrogen compared to pure methane, and the maximum energy stored in the storage tank for pure hydrogen is approximately 28% lower compared to methane, whereas the total entropy generation for pure hydrogen is approximately 52% higher compared to pure methane.