This article deals with the Bayesian and non-Bayesian estimation of reliability of an s-out-of-k system with identical component strengths which are subjected to a common stress. Assuming that both stress and strength are assumed to have an exponentiated Pareto distribution with known and unequal shape parameters (1, 2). Five non-Bayesian methods of estimation will be used which are maximum likelihood, moments, percentile, least squares and weighted least squares. The Bayesian estimation will be studied under squared error and LINEX loss functions using Lindley's approximation. Based on a Monte Carlo simulation study, comparisons are made between the different estimators of system reliability by obtaining their absolute biases and mean squared errors. Comparison study revealed that the maximum likelihood estimator works the best among the competitors.