In India, COVID-19 (CoronaVirusDisease-2019) continues to this day, although with subdued intensity, following two major waves of viral infection. Despite ongoing vaccination drives to curb the spread of COVID-19, the relative potential of the administered vaccines to render immune protection to the general population and their advantage over natural infection remain undocumented. In this study, we examined the humoral and cell-mediated immune responses induced by the two vaccines Covishield and Covaxin, in individuals living in and around Kolkata, India. We also compared the immune responses induced separately by vaccination and natural infection. Our results indicate that although Covishield generates a better humoral immune response toward SARS-CoV-2, both vaccines are almost equivalent in terms of cell-mediated immune response to the virus. Both Covishield and Covaxin, however, are more effective toward the wild-type virus than the Delta variant. Additionally, the overall immune response resulting from natural infection in and around Kolkata is not only similar to that generated by vaccination but the cell-mediated immune response to SARS-CoV-2 also lasts for at least ten months in some individuals after the viral infection.