We investigate by Monte Carlo simulations the frequency dependent conductivity sigma(omega,T) and the spin lattice relaxation rate 1/T-1(omega,T) due to the hopping motion of noninteracting particles in an uncorrelated and correlated disordered energy landscape. The conductivity shows a pronounced dispersion at low temperatures in both the correlated and the uncorrelated case, reminiscent of the non-Debye behavior observed in many disordered materials. In contrast, 1/T-1(omega,T) exhibits the typical non-BPP form for uncorrelated energy disorder, but obeys an ordinary BPP-type behavior in the presence of finite correlations. Our results show that in general a simple relation between sigma(omega,T) and 1/T-1(omega,T) does not exist and that it might be difficult to account for the experimental findings, if interactions between the mobile particles are neglected.