The radiative energy loss of a relativistic charge in a dense, absorptive medium can be affected significantly by damping phenomena. The effect is more pronounced for large energies of the charge and/or large damping of the radiation. This can be understood in terms of a competition between the formation time of bremsstrahlung and a damping time scale. Discussing this competition in detail for the absorptive QED and QCD medium, we identify the regions in energy and parameter space, in which either coherence or damping effects are of major importance for the radiation spectrum. We show that damping mechanisms lead to a stronger suppression of the spectrum than coherence effects. This might be visible experimentally in correlations between hadrons at large momenta.