The predictions of binary classical nucleation theory for a surface active system are compared with results obtained from density functional calculations. It is found that the unphysical predictions produced by the classical theory are connected to a large disparity of vapor and liquid mole fractions in the equilibrium diagram. In this regime, density functional nuclei show, when the vapor mole fraction is held fixed, very different compositions in the center of the nucleus at low and high vapor densities, although the surface layer density profiles are qualitatively very similar. The classical theory, on the other hand, is not able to account for the compositional differences of the nuclei. However, it is found that the classical theory is able to predict the slopes of nucleation rate versus vapor density correctly when the vapor mole fraction is held constant. It is shown that this is equivalent to a correct prediction of the total number, n(1)+n(2), of molecules in the nucleus.