We show that a previously reported discrepancy between simulations of superconducting Josephson junction arrays and the theoretical analysis of Ambegaokar, Halperin, Nelson, and Siggia (AHNS)[Phys. Rev. Lett. 40, 783 (1978)] is rooted in a peculiar finite-size effect under periodic boundary conditions. Our simulation results for the largest array support the power-law I-V curves predicted by AHNS. Analysis of the vortex dynamics reveals two intrinsic length scales set by the applied current, which define three size regimes with distinctive I-V characteristics.