First principles calculations of the vibrational, thermodynamic and mechanical properties of the Ni-Ti-Sn Heusler and half-Heusler compounds have been performed. First, we have calculated the Raman and infrared spectra of NiTiSn, providing benchmark theoretical data directly useful for the assignments of its experimental spectra and clarifying the debate reported in the literature on the assignment of its modes. Then, we have discussed the significant vibrational density-of-states of Ni2TiSn at low-frequencies. These states are at the origin of (i) its smaller free energy, (ii) its higher entropy, and (iii) its lower Debye temperature, with respect to NiTiSn. Finally, we have reported the mechanical properties of the two compounds. In particular, we have found that the half-Heusler compound has the largest stiffness. Paradoxically, its bulk modulus is also the smallest. This unusual behavior has been related to the Ni-vacancies that weaken the structure under isostatic compression. Both compounds show a ductile behavior.