A numerical study based on the multiconfiguration time-dependent Hartree (MCTDH) method for the propagation of density operators is presented. Within the MCTDH framework, there exist two types of expansions of the density operator which employ different kinds of so-called single-particle density operators. The latter may either represent Hermitian operators (type I), or else ket-bra products of so-called single-particle functions (type II). The performance of these two types of representations is tested on three models for closed and open system dynamics. The open dynamics is induced for each system by Lindblad-type dissipation operators. We find that the MCTDH representation of type I is most efficient if the coupling between the degrees of freedom is weak, but if the temperature of the initial state and/or the strength of the dissipation is moderate. On the other hand, for strong coupling between the degrees of freedom, but for lower temperatures and for weak dissipation type II is more efficient. Furthermore, considering the open dynamics of the systems both types of MCTDH density operators can be very efficiently used to calculate absorption spectra. The Lindblad-type dissipation operator is shown, however, to capture only partially the effects of a real environment.