Stochastic responses in power systems contain mode information of low-frequency oscillations. This paper compares three methods:Auto-Correlation analysis (AC), Natural Excitation Technique (NExT) and Random Decrement Technique (RDT), which are applied to extract system free oscillation response from stochastic response, and then estimates mode frequencies and damping ratios using Eigensystem Realization Algorithm (ERA). Monte Carlo simulations are carried out in the four-generator two-area system and the New England system, and the estimation performance and applicability of the three methods are compared and analyzed from the aspects of length of time window, noise level, mode damping condition and multi-channel stochastic responses. Simulation results show that the extraction of free response by means of AC has better adaptability, and the mode estimation results are more accurate than the methods based on NExT and RDT.