The approved coronavirus disease (COVID-19) vaccines reduce the risk of disease by 70-95%; however, their efficacy in preventing COVID-19 is unclear. Moreover, the limited vaccine supply raises questions on how they can be used effectively. To examine the optimal allocation of COVID-19 vaccines in South Korea, we constructed an age-structured mathematical model, calibrated using country-specific demographic and epidemiological data. The optimal control problem was formulated with the aim of finding time-dependent age-specific optimal vaccination strategies to minimize costs related to COVID-19 infections and vaccination, considering a limited vaccine supply and various vaccine effects on susceptibility and symptomatology. Our results suggest that "susceptibility-reducing" vaccines should be relatively evenly distributed among all age groups, resulting in more than 40% of eligible age groups being vaccinated. In contrast, "symptom-reducing" vaccines should be administered mainly to individuals aged 20-29 and >/=60 years. Thus, our study suggests that the vaccine profile should determine the optimal vaccination strategy. Our findings highlight the importance of understanding vaccine's effects on susceptibility and symptomatology for effective public health interventions.