Equilibrium physical properties of the solid and liquid phases of parahydrogen, computed by first principle computer simulations, are compared for different choices of pair-wise, spherically symmetric intermolecular potentials. The most recent ab initio potential [Patkowski et al., J. Chem. Phys., 2008, 129, 094304], which has a stiffer repulsive core than the commonly used Silvera-Goldman, yields results for structural quantities in better agreement with the most recent experimental measurements, while possibly overestimating the kinetic energy per molecule by as much as 10%. Altogether, the comparison between theory and the available experimental evidence suggests that the potential of Patkowski et al. may be a better choice for simulations of condensed phases of parahydrogen at moderate pressure.