Abstract: Bimetallic plasmonic nanoparticles enable tuning of the optical response and chemical stability by variation of the composition. The present numerical simulation study compares Ag–Au alloy, Ag@Au core–shell, and Au@Ag core–shell bimetallic plasmonic nanoparticles of both spherical and anisotropic (nanotriangle and nanorods) shapes. By studying both spherical and anisotropic (with LSPR in the near-infrared region) shapes, cases with and without interband transitions of Au can be decoupled. Explicit comparisons are facilitated by numerical models supported by careful validation and examination of optical constants of Au–Ag alloys reported in the literature. Although both Au–Ag core–shell and alloy nanoparticles exhibit an intermediary optical response between that of pure Ag and Au nanoparticles, there are noticeable differences in the spectral characteristics. Also, the effect of the bimetallic constitution in anisotropic nanoparticles is starkly different from that in spherical nanoparticles due to the absence of Au interband transitions in the former case. In general, the improved chemical stability of Ag nanoparticles by incorporation of Au comes with a cost of reduction in plasmonic enhancement, also applicable to anisotropic nanoparticles with a weaker effect. A photothermal heat transfer study confirms that increased absorption by the incorporation of Au in spherical Ag nanoparticles also results in an increased steady-state temperature. On the other hand, anisotropic nanoparticles are inherently better absorbers and hence better photothermal sources, and their photothermal properties are apparently not strongly affected by the incorporation of one metal in the other. This study of the optical/spectral and photothermal characteristics of bimetallic Au–Ag alloy versus core–shell nanoparticles provides detailed physical insight for development of new taylor-made plasmonic nanostructures.