In this comprehensive assessment of basis-set behavior for the XSAPT, SAPT0, and SAPT0(KS) methods, we have demonstrated that the energy components E elst , E exch , E ind , and E disp converge in different ways with respect to the underlying Gaussian basis set. The XSAPT approach replaces conventional second-order dispersion with a model that is both cheaper and more accurate: either MBD, or else ai D3. The former is a first-principles, density-dependent description of dispersion, but one that substantially mitigates the basis-set dependence of E disp , which for XSAPT + MBD is converged (or nearly converged) already in double-ζ basis sets. In XSAPT + ai D3, the classical dispersion potential has no basis-set dependence at all. In contrast, for conventional SAPT or MP2 calculations, dispersion exhibits the slowest convergence with respect to basis set amongst all the energy components; this was a motivating factor in the early development of XSAPT. With the basis-set dependence of E disp thus rendered manageable, it is no longer clear that a compromise (or "Pauling-point") basis set such as jun-cc-pVDZ, which is often used for conventional SAPT0, is the best choice for hybrid XSAPT-type methods. Much of the present work has therefore been dedicated to finding basis sets that afford converged results for all four energy components. A general trend across all of the energy components is that diffuse functions are important, even in systems where the monomers are charge-neutral. This is an important observation, given that (in our experience) many computational chemists are hesitant to include diffuse functions, presumably for reasons of cost. Data presented herein make it clear that this omission has deleterious consequences for accuracy. Notably, this is true for the perturbative components of XSAPT (E elst , E exch , and E ind ) that have identical forms as compared to the SAPT0 method, hence our results underscore the need for diffuse functions in conventional SAPT calculations as well.