The European electricity industry, the dominant sector of the world's largest cap-and-trade scheme, is one of the most-studied examples of carbon pricing. In particular, numerical models are often used to study the uncertain future development of carbon prices and emissions. While parameter uncertainty is often addressed through sensitivity analyses, the potential uncertainty of the models themselves remains unclear from existing single-model studies. This study investigates such model-related uncertainty by running a structured model comparison experiment, which exposes five numerical power sector models to aligned input parameters—finding stark model differences. At a carbon price of 27 EUR/t in 2030, the models estimate that European power sector emissions will decrease by 36–57% when compared to 2016. Most of this variation can be explained by the extent to which models consider the market-driven decommissioning of coal- and lignite-fired power plants. Higher carbon prices of 57 and 87 EUR/t yield a stronger decrease in carbon emissions, by 45–75% and 52–80%, respectively. The lower end of these ranges can be attributed to the short-term fuel switch captured by dispatch-only models. The higher reductions correspond to models that additionally consider market-based investment in renewables. By further studying cross-model variation in the remaining emissions at high carbon prices, the representation of combined heat and power is identified as another crucial driver of differences across model results.