The homogeneous vapor-liquid nucleation of argon has been explored at T=70 and 90 K using classical nucleation theory, semiempirical density functional theory, and Monte Carlo simulations using the aggregation-volume-bias algorithm with umbrella sampling and histogram-reweighting. In contrast with previous simulation studies, which employed only the Lennard-Jones intermolecular potential, the current studies were carried out using various pair potentials including the Lennard-Jones potential, a modified Buckingham exponential-six potential, the Barker-Fisher-Watts pair potential, and a recent ab initio potential developed using the method of effective diameters. It was found that the differences in the free energy of formation of the critical nuclei between the potentials cannot be explained solely in terms of the difference in macroscopic properties of the potentials, which gives a possible reason for the failure of classical nucleation theory.