[en] An investigation of the hadronic final state in diffractive and non-diffractive deep-inelastic electron-proton scattering at HERA is presented, where diffractive data are selected experimentally by demanding a large gap in pseudo-rapidity around the proton remnant direction. The transverse energy flow in the hadronic final state is evaluated using a set of estimators which quantify topological properties. Using available Monte Carlo QCD calculations, it is demonstrated that the final state in diffractive DIS exhibits the features expected if the interaction is interpreted as the scattering of an electron off a current quark with associated effects of perturbative QCD. A model in which deep-inelastic diffraction is taken to be the exchange of a pomeron with partonic structure is found to reproduce the measurements well. Models for deep-inelastic ep scattering, in which a sizeable diffractive contribution is present because of non-perturbative effects in the production of the hadronic final state, reproduce the general tendencies of the data but in all give a worse description. (orig.)