We present a detailed experimental study on Mo1-xSix thin films, an archetypal alloy system combining metallic and semiconductor materials. The correlations between structure and elastic response are comprehensively investigated. We focus on assessing trends for understanding the evolution of elastic properties upon Si alloying in relation to the structural state (crystalline vs amorphous), bonding character (metallic vs covalent), and local atomic environment. By combining picosecond ultrasonics and Brillouin light scattering techniques, a complete set of effective elastic constants and mechanical moduli (B, G, E) is provided in the whole compositional range, covering bcc solid solutions (x < 0.20) and the amorphous phase (0.20 < x < 1.0). A softening of the shear and Young moduli and a concomitant decrease of the Debye temperature is revealed for crystalline alloys, with a significant drop being observed at x similar to 0.2 corresponding to the limit of crystal lattice stability. Amorphous alloys exhibit a more complex elastic response, related to variations in coordination number, atomic volume, and bonding state, depending on Si content. Finally, distinct evolutions of the G/B ratio as a function of Cauchy pressure are reported for crystalline and amorphous alloys, enabling us to identify signatures of ductility vs brittleness in the features of the local atomic environment. This work paves the way to design materials with improved mechanical properties by appropriate chemical substitution or impurity incorporation during thin-film growth.