A parallel study of the radical copper enzyme galactose oxidase (GOase) and a low molecular weight analog of the active site was performed with dynamical density functional and mixed quantum-classical calculations. This combined approach enables a direct comparison of the properties of the biomimetic and the natural systems throughout the course of the catalytic reaction. In both cases, five essential forms of the catalytic cycle have been investigated: the resting state in its semi-reduced (catalytically inactive) and its oxidized (catalytically active) form, A(semi) and A(ox), respectively; a protonated intermediate B; the transition state for the rate-determining hydrogen abstraction step C, and its product D. For A and B the electronic properties of the biomimetic compound are qualitatively very similar to the ones of the natural target. However, in agreement with the experimentally observed difference in catalytic activity, the calculated activation energy for the hydrogen abstraction step is distinctly lower for GOase (16 kcal/mol) than for the mimetic compound (21 kcal/mol). The enzymatic transition state is stabilized by a delocalization of the unpaired spin density over the sulfur-modified equatorial tyrosine Tyr272, an effect that for geometric reasons is essentially absent in the biomimetic compound. Further differences between the mimic and its natural target concern the structure of the product of the abstraction step, which is characterized by a weakly coordinated aldehyde complex for the latter and a tightly bound linear complex for the former.