We perform head-on collision simulations of compact dark matter subhalos using distinct numerical methods for fuzzy dark matter (FDM) and cold dark matter (CDM) models.For FDM, we solve the Schrodinger-Poisson equations with a pseudospectral solver, while for CDM, we utilize a smoothed particle hydrodynamics N-body code. Our results show that velocity decrease of subhalos is significantly greater in FDM model than in CDM, particularly at lower initial velocities, attributed to gravitational cooling-a unique mechanism of stabilizing in FDM with dissipating kinetic energy.This stark contrast in energy dissipation between two DM models suggests that FDM may offer valuable insights into understanding the dynamic behaviors of DM during galaxy cluster collisions, such as those observed in the Bullet cluster and Abell 520.These findings strongly suggest that FDM is not only capable of explaining these complex astrophysical phenomena but also serves as a compelling alternative to the traditional CDM model, offering resolutions to longstanding discrepancies in DM behavior.