Moving towards carbon-neutral societies, both nuclear and renewable energy can potentially supply CO2-free electricity. While the cost of renewable energy has decreased significantly, the cost of nuclear has, however, increased in the past decades and now in general exceeds the cost of renewables. However, one cannot compare directly the per unit cost of electricity since temporal behavior in the electricity production differs substantially between the two groups of technologies. Nuclear power inherently aims to provide a constant base load supply of electricity, while renewables generally depend on weather patterns. Thus, the two have different requirements and impact the overall system costs differently regarding flexibility and system design. Focusing on the case of Denmark, this article investigates a future fully sector-coupled energy system in a carbon-neutral society and compares the operation and costs of renewables and nuclear-based energy systems. The study finds that investments in flexibility in the electricity supply are needed in both systems due to the constant production pattern of nuclear and the variability of renewable energy sources. However, the scenario with high nuclear implementation is 1.2 billion EUR more expensive annually compared to a scenario only based on renewables, with all systems completely balancing supply and demand across all energy sectors in every hour. For nuclear power to be cost competitive with renewables an investment cost of 1.55 MEUR/MW must be achieved, which is substantially below any cost projection for nuclear power.