Kerogen has a lower affinity to hydrogen than methane; thus, it allows hydrogen to flow more easily, but it is unclear how the permeabilities of hydrogen and methane differ. This study determines the single-phase permeability of hydrogen and compares it with methane permeability in organic-rich caprock. It takes into account adsorption to the pore wall and slippage at the boundary. It implements the two processes at 370 K for pressures from 500 to 4000 psi to obtain the hydraulic conductance of a sub-100-nm conduit. It then relates them to the macroscopic behavior via network modeling. Lower pressures represent depleted gas reservoirs in the subsurface. Decreasing pore pressure enhances hydrogen transport by reducing its adsorption to the pore wall and transitioning its behavior from continuum to discrete particles, leading to first- or second-order slippage. The results show that hydrogen conductance, qin−situ (H2), is always larger than the reference conductance without adsorption and slippage (q0). Hydrogen permeability, kin−situ (H2), is also larger than methane permeability, kin−situ (CH4), while the permeability values differ by 70% − 130%, depending on the pore pressure. This study also determines the conduit size corresponding to the ratio of hydrogen permeability to methane permeability at in-situ conditions by comparing it with the ratio of hydraulic conductance of hydrogen to methane. The results have applications in underground hydrogen storage by indicating how hydrogen flow changes with pressure in ultra-tight formations.