We have carried out first principles calculations of the vibrational and thermodynamic behavior in NiSi and isostructural compound NiGe. Phonon density of states has also been measured in NiSi using inelastic neutron scattering techniques. We find that the vibrational spectra of the two compounds are very different, due to the difference in the size and mass of Si and Ge. Interesting anomalous thermal behavior of NiSi due to anharmonic phonons is brought out well in our calculations, particularly the negative thermal expansion (NTE) along the b-axis of the orthorhombic unit cell. Large difference in thermal expansion behavior of NiSi and NiGe is very well reproduced by the calculations. Additionally, calculations enable to identify the phonon modes which lend major contribution to the negative thermal expansion behavior in NiSi, and reasons for negligible NTE in NiGe. Such typical representative modes at the zone-boundary along b-axis involve transverse vibrations of Si/Ge along c-axis.