The possibility to control electrokinetic transport through carbon and hexagonal boron nitride (hBN) nanotubes has recently opened new avenues for nanofluidic approaches to face outstanding challenges such as energy production and conversion or water desalination. The pH-dependence of experimental transport coefficients point to the sorption of hydroxide ions as the microscopic origin of the surface charge and recent ab initio calculations suggest that these ions behave differently on carbon and hBN, with only physisorption on the former and both physi-and chemisorption on the latter. Using classical non-equilibrium molecular dynamics simulations of interfaces between an aqueous electrolyte and three models of hBN and graphite surfaces, we demonstrate the major influence of the sorption mode of hydroxide ions on the interfacial transport properties. Physisorbed surface charge leads to a considerable enhancement of the surface conductivity as compared to its chemisorbed counterpart, while values of the z-potential are less affected. The analysis of the MD results for the surface conductivity and z-potential in the framework of Poisson-Boltzmann-Stokes theory, as is usually done to analyze experimental data, further confirms the importance of taking into account both the mobility of surface hydroxide ions and the decrease of the slip length with increasing titratable surface charge density.