The magnetic properties of maghemite (gamma-Fe2O3) cubic and spherical nanoparticles of similar sizes have been experimentally and theoretically studied. The blocking temperature, TB, of the nanoparticles depends on their shape, with the spherical ones exhibiting larger TB. Other low temperature properties such as saturation magnetization, coercivity, loop shift or spin canting are rather similar. The experimental effective anisotropy and the Monte Carlo simulations indicate that the different random surface anisotropy of the two morphologies combined with the low magnetocrystalline anisotropy of gamma-Fe2O3 is the origin of these effects.