This paper addresses ordinal comparison in the simulation of discrete-event systems. It examines dynamic behaviors of ordinal comparison in a fairly general framework. It proves that for regenerative systems, the probability of obtaining a desired solution using ordinal comparison approaches converges at exponential rate, while the variances of the performance measures converge at best at rate O(1/t(2)), where t is the simulation time. Heuristic arguments are provided to explain that exponential convergence holds for general systems.