We performed isothermal-isobaric molecular dynamics simulations to study the effects of host-guest asymmetries on the thermophysical and structural properties of methane and carbon dioxide sI clathrate hydrates. In particular, we analyzed the effect of the strength of the host-guest interactions in realistic molecular descriptions of the host intermolecular potentials, the effect of the type of water intermolecular potential, and the degree of cage occupancy on the resulting properties of the hydrates. Finally, we used the simulation results to interpret the limitations and implications of the main assumptions behind the original vdWP theory of clathrates and its current modifications, which are used in the modeling of hydrate phase equilibria.