Continuous surveillance is critical for early intervention against emerging novel SARS-CoV-2 variants. Therefore, we investigated and compared the variant-specific evolutionary epidemiology of all the Delta and Omicron sequences collected between 2021 and 2023 in Kuwait. We used Bayesian phylodynamic models to reconstruct, trace, and compare the two variants’ demographics, phylogeographic, and host characteristics in shaping their evolutionary epidemiology. The Omicron had a higher evolutionary rate than the Delta. Both variants underwent periods of sequential growth and decline in their effective population sizes, likely linked to intervention measures and environmental and host characteristics. We found that the Delta strains were frequently introduced into Kuwait from East Asian countries between late 2020 and early 2021, while those of the Omicron strains were most likely from Africa and North America between late 2021 and early 2022. For both variants, our analyses revealed significant transmission routes from patients aged between 20 and 50 years on one side and other age groups, refuting the notion that children are superspreaders for the disease. In contrast, we found that sex has no significant role in the evolutionary history of both variants. We uncovered deeper variant-specific epidemiological insights using phylodynamic models and highlighted the need to integrate such models into current and future genomic surveillance programs.