We show that in most interesting cases where infinitesimal perturbation analysis (IPA) applies for derivative estimation, a finite-difference scheme with common random numbers (FDC) has the same order of convergence, namely O (n^-1/2), provided that the size of the finite-difference interval converges to zero fast enough. This holds for both one-sided and two-sided FDC. This also holds for different variants of IPA, like for smooted perturbation analysis (SPA), which is based on conditional expectation. We give some examples and numerical illustrations. Besides their theoretical interest, these results might have practical implications for situations where inplementing IPA is more difficult than simply doing finite differences.