In crystalline solar cells, the substrate itself constitutes a large portion of the fabrication cost as it is derived from semiconductor ingots grown in costly high temperature processes. Thinner wafer substrates allow some cost saving as more wafers can be sliced from a given ingot, although technological limitations in slicing or sawing of wafers off an ingot, as well as the physical strength of the sliced wafers, put a lower limit on the substrate thickness. Complementary to these economical and techno-physical points of view, a device operation point of view of the substrate thickness would be useful. With this in mind, BC-BJ Si and GaAs solar cells are compared one to one by means of the Medici device simulation, with a particular emphasis on the substrate thickness. Under ideal conditions of 0.6 ${mu}m$ photons entering the 10 ${mu}m$-wide BC-BJ solar cells at the normal incident angle (${ heta}=90^{circ}$), GaAs is about 2.3 times more efficient than Si in terms of peak cell power output: 42.3 $mW{cdot}cm^{-2}$ vs. 18.2 $mW{cdot}cm^{-2}$. This strong performance of GaAs, though only under ideal conditions, gives a strong indication that this material could stand competitively against Si, despite its known high material and process costs. Within the limitation of the minority carrier recombination lifetime value of $5{ imes}10^{-5}$ sec used in the device simulation, the solar cell power is known to be only weakly dependent on the substrate thickness, particularly under about 100 ${mu}m$, for both Si and GaAs. Though the optimum substrate thickness is about 100 ${mu}m$ or less, the reduction in the power output is less than 10% from the peak values even when the substrate thickness is increased to 190 ${mu}m$. Thus, for crystalline Si and GaAs with a relatively long recombination lifetime, extra efforts to be spent on thinning the substrate should be weighed against the expected actual gain in the solar cell output power.