Molecular dynamics simulation techniques are used to analyze damage production in Ge by the thermal spikes process and to compare the results to those obtained for Si. As simulation results are sensitive to the choice of the inter-atomic potential, several potentials are compared in terms of material properties relevant for damage generation, and the most suitable potentials for this kind of analysis are identified. A simplified simulation scheme is used to characterize, in a controlled way, the damage generation through the local melting of regions in which energy is deposited. Our results show the outstanding role of thermal spikes in Ge, since the lower melting temperature and thermal conductivity of Ge make this process much more efficient in terms of damage generation than in Si. The study is extended to the modeling of full implant cascades, in which both collision events and thermal spikes coexist. Our simulations reveal the existence of bigger damaged or amorphous regions in Ge than in Si, which may be formed by the melting and successive quenching induced by thermal spikes. In the particular case of heavy ion implantation, defect structures in Ge are not only bigger, but they also present a larger net content in vacancies than in Si, which may act as precursors for the growth of voids and the subsequent formation of honeycomb-like structures.