To tackle emerging power system small-signal stability problems such as wideband oscillations induced by the large-scale integration of renewable energy and power electronics, it is crucial to review and compare existing small-signal stability analysis methods. On this basis, guidance can be provided on determining suitable analysis methods to solve relevant small-signal stability problems in power electronics-dominated power systems (PEDPSs). Various mature methods have been developed to analyze the small-signal stability of PEDPSs, including eigenvalue-based methods, Routh stability criterion, Nyquist/Bode plot based methods, passivity-based methods, positive-net-damping method, lumped impedance-based methods, bifurcation-based methods, etc. In this paper, the application conditions, advantages, and limitations of these criteria in identifying oscillation frequencies and stability margins are reviewed and compared to reveal and explain connections and discrepancies among them. Especially, efforts are devoted to mathematically proving the equivalence between these small-signal stability criteria. Finally, the performance of these criteria is demonstrated and compared in a 4-machine 2-area power system with a wind farm and an IEEE 39-bus power system with 3 wind farms.