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This paper investigates the seismic response of a rigid and flexible RC building by performing nonlinear time history analysis (NLTHA). In the present study, the numerical model of a 5-storey monolithic RC (MRC) and 5-storey precast RC (PRC) buildings are developed in SAP2000. The buildings are assumed to be situated in Assam and a real Silchar site from Assam is considered. For the NLTHA, six spectrum compatible time histories (SCTH) are considered. The first set comprises of 3 SCTH matched to the Indian seismic code design spectra (ISCDS) and the second set comprises of 3 SCTH matched to the site-specific elastic response spectra (SSERS). The NLTHA results show that the roof displacement of the MRC building is less as compared to the PRC building for all the considered cases. However, the response for both the structures for SSERS compatible time histories is more significant as compared to the ISCDS compatible time histories. It is interesting to note that when the energy dissipation in the structure is evaluated for ISCDS compatible time histories, the damage in PRC building is negligible as compared to MRC building. Moreover, for SSERS compatible time histories, the damage in both the buildings are comparable. The results show the importance of site-specific study and its response on the structure behavior.