A comparative analysis is carried out of the growth peculiarities under molecular-beam epitaxy of germanium quantum dots on the silicon surfaces with different crystallographic orientations Si(100) and Si(111), including the case of the presence of tin surfactant on the surface. The free energy change, activation barrier of nucleation, critical thickness of the transition from two-dimensional growth to three-dimensional one, as well as the surface density and size distribution function of quantum dots in these systems are calculated.