The effects of confinement on biexciton renormalization in self-assembled InAs and interfacial GaAs quantum dot (QD) ensembles are studied using two-dimensional Fourier-transform spectroscopy. We find that in thermally annealed InAs QDs, changes in the biexciton transition energy are strongly correlated with those of the exciton and that the biexciton binding energy is similar for all QDs in the ensemble. These results are in contrast to those from GaAs QDs formed from interfacial fluctuations of a narrow quantum well (QW). In both the GaAs QW and QDs, correlation is reduced and the biexciton binding exhibits a strong dependence on localization. Comparison with simulations reveals how confinement and Coulomb interactions modify biexciton renormalization.