Two of the COVID-19 vaccines currently approved in the United States require two doses, administered three to four weeks apart. Constraints in vaccine supply and distribution capacity, together with a deadly wave of COVID-19 from November 2020 to January 2021 and the emergence of highly contagious SARS-CoV-2 variants, sparked a policy debate on whether to vaccinate more individuals with the first dose of available vaccines and delay the second dose, or to continue with the recommended two-dose series as tested in clinical trials. We developed an agent-based model of COVID-19 transmission to compare the impact of these two vaccination strategies, while varying the temporal waning of vaccine efficacy following the first dose and the level of pre-existing immunity in the population. Our results show that for Moderna vaccines, a delay of at least 9 weeks could maximize vaccination program effectiveness and avert at least an additional 17.3 (95% CrI: 7.8 - 29.7) infections, 0.71 (95% CrI: 0.52 - 0.97) hospitalizations, and 0.34 (95% CrI: 0.25 - 0.44) deaths per 10,000 population compared to the recommended 4-week interval between the two doses. Pfizer-BioNTech vaccines also averted an additional 0.61 (95% CrI: 0.37 - 0.89) hospitalizations and 0.31 (95% CrI: 0.23 - 0.45) deaths per 10,000 population in a 9-week delayed second dose strategy compared to the 3-week recommended schedule between doses. However, there was no clear advantage of delaying the second dose with Pfizer-BioNTech vaccines in reducing infections, unless the efficacy of the first dose did not wane over time. Our findings underscore the importance of quantifying the characteristics and durability of vaccine-induced protection after the first dose in order to determine the optimal time interval between the two doses.