Plasmonic metal nanoparticles have great potential for chemical and biological sensor applications, due to their sensitive spectral response to the local environment of the nanoparticle surface and ease of monitoring the light signal due to their strong scattering or absorption. In this work, we investigated the dependence of the sensitivity of the surface plasmon resonance (frequency and bandwidth) response to changes in their surrounding environment and the relative contribution of optical scattering to the total extinction, on the size and shape of nanorods and the type of metal, that is, Au vs Ag. Theoretical consideration on the surface plasmon resonance condition revealed that the spectral sensitivity, defined as the relative shift in resonance wavelength with respect to the refractive index change of surrounding materials, has two controlling factors: first the bulk plasma wavelength, a property dependent on the metal type, and second on the aspect ratio of the nanorods which is a geometrical parameter. It is found that the sensitivity is linearly proportional to both these factors. To quantitatively examine the dependence of the spectral sensitivity on the nanorod metal composition and the aspect ratio, the discrete dipole approximation method was used for the calculation of optical spectra of Ag-Au alloy metal nanorods as a function of Ag concentration. It is observed that the sensitivity does not depend on the type of the metal but depends largely on the aspect ratio of nanorods. The direct dependence of the sensitivity on the aspect ratio becomes more prominent as the size of nanorods becomes larger. However, the use of larger nanoparticles may induce an excessive broadening of the resonance spectrum due to an increase in the contribution of multipolar excitations. This restricts the sensing resolution. The insensitivity of the plasmon response to the metal composition is attributable to the fact that the bulk plasma frequency of the metal, which determines the spectral dispersion of the real dielectric function of metals and the surface plasmon resonance condition, has a similar value for the noble metals. On the other hand, nanorods with higher Ag concentration show a great enhancement in magnitude and sharpness of the plasmon resonance band, which gives better sensing resolution despite similar plasmon response. Furthermore, Ag nanorods have an additional advantage as better scatterers compared with Au nanorods of the same size.