Molecular simulations have been used to evaluate the effect exerted by metal centres on the adsorption and diffusion of hydrogen in metal-organic frameworks. Simulations were carried out for the MIL-53 (Cr and Al) structures and the isostructural vanadium analogue MIL-47 at room temperature. To validate the models and force fields used in this work, the adsorption isotherms, energies and entropies, and self-diffusivities in Cu-BTC and IRMOF-1 metal-organic frameworks were computed. Using the validated force fields and models, a detailed analysis of the preferential adsorption sites is reported, allowing the energetic contribution in the low-coverage regime (Henry constants and adsorption energies and entropies) to be determined as a function of loading (adsorption isotherms). The influence of each energetic contribution to the charged and uncharged models of hydrogen has also been analyzed.