Photoexcited nonthermal electrons and holes in metallic nanoparticles, known as hot carriers, can be judiciously harnessed to drive interesting photocatalytic molecule-transforming processes on nanoparticle surfaces. Interband hot carriers are generated upon direct photoexcitation of electronic transitions between different electronic bands, whereas intraband hot carriers are derived from nonradiative decay of plasmonic electron oscillations. Due to their fundamentally distinct photogeneration mechanisms, these two types of hot carriers differ strikingly from each other in terms of energy distribution profiles, lifetimes, diffusion lengths, and relaxation dynamics, thereby exhibiting remarkably different photocatalytic behaviors. The spectral overlap between plasmon resonances and interband transitions has been identified as a key factor that modulates the interband damping of plasmon resonances, which regulates the relative populations, energy distributions, and photocatalytic efficacies of intraband and interband hot carriers in light-illuminated metallic nanoparticles. As exemplified by the Au-Cu alloy nanoparticles investigated in this work, both the resonant frequencies of plasmons and the energy threshold for the d-to-sp interband transitions can be systematically tuned in bimetallic alloy nanoparticles by varying the compositional stoichiometries and particle sizes. Choosing photocatalytic degradation of Rhodamine B as a model reaction, we elaborate on how the variation of the particle sizes and compositional stoichiometries profoundly influences the photocatalytic efficacies of interband and intraband hot carriers in Au-Cu alloy nanoparticles under different photoexcitation conditions.