We theoretically and comparatively study the performance of spherical and cylindrical conductive thermal diodes operating with a phase-change material, whose thermal conductivity significantly changes in a narrow interval of temperatures. Simple analytical expressions are derived for the temperature profiles, heat flows and optimal rectification factors of both diodes. It is shown that the diode geometry has a strong impact on the temperatures and heat flows, but not so much on the diode rectification factor. Optimal rectification factors of 20.8% and 20.7% are obtained for the spherical and cylindrical diodes operating with a temperature difference of 376−300 = 76 K and 376.5-300 = 76.5 K between the terminals of VO2 and a phase invariant material, respectively. These similar rectification factors could be enhanced with a material thermal conductivity exhibiting a higher contrast than that of VO2. The obtained results can thus be useful to guide the development of phase-change materials able to optimize the rectification of conductive thermal diodes with different geometries.