The comparison of empirical Bayes and generalized maximum likelihood estimates of reliability performances is made in terms of risk efficiencies when the data are progressively Type II censored from Rayleigh distribution. The empirical Bayes estimates are obtained using an asymmetric loss function. The risk functions of the estimates and risk efficiencies are obtained under this loss function. A real data set is presented to illustrate the proposed comparison method, and the performance of the estimates is examined and compared in terms of risk efficiencies by means of Monte Carlo simulations. The simulation results indicate that the proposed empirical Bayes estimates are more preferable than the generalized maximum likelihood estimates.