Gold-silver and silver-gold core-shell nanoparticle dimers were studied based on their extinction cross-section spectrum and bulk refractive index sensitivity. The simulations were performed by using the boundary element method (BEM) and the polarization direction of the used plane-wave excitation was parallel with the symmetry axis. The running parameters were the particles’ outer and inner radii and their (interparticle gap/full diameter). For different particle sizes and distances, the shape of the spectra and the refractive index sensitivities are presented. In the extinction spectra, the observable peaks originate from either the gold or silver components and the most intense peak position can be distinctly assigned to one of them. A sharp boundary separates these two regions in the plane of the core radius and shell thickness parameters. It was found that by decreasing the interparticle gap, the boundary line between these two regions shifts towards the thinner shells for Ag@Au dimers, while it shifts towards the smaller cores for Au@Ag dimers. Since the sensitivity of peaks corresponding to the Au and Ag components are significantly different, the presented data can help optimize interparticle gaps concerning the core/shell thicknesses to maximize the sensitivity of nanoparticle dimers.