Using panel data of Chinese cities from 2006 to 2020, this study constructs the carbon emission performance index from the perspective of the dual differences in the four stages of growth, maturity, decline and regeneration of eastern, central, western and resource-based cities (RBCs). This study employs the Dagum Gini coefficient and kernel density estimation to explore σ convergence and β convergence for understanding the dual differences, dynamic evolutionary trend and convergence. Results indicate that during the sample period, the carbon emission performance index of RBCs shows a fluctuating upward trend with regional and typological imbalance influenced by geographical location and division of labour. The carbon emission performance index of RBCs of different regions and types (Growing, Mature, Declining and Regenerative) shows a fluctuating downward trend. However, the carbon emission performance index gap between the 116 RBCs in China is gradually expanding, further corroborating the influence of “excellent but outliers”. The overall level of carbon emission performance index of RBCs exhibits σ convergence, absolute β convergence and conditional β convergence phenomena. Notably, growing and regenerative RBCs demonstrate a clear “catching-up” trend compared to mature and declining RBCs. Furthermore, the inclusion of control variables reveals varying degrees of increased convergence speed. Environmental regulation intensity (ERI), gross domestic product (GDP), energy consumption structure (ECS), technology development level (T), industrial structure (IS) and foreign direct investment demonstrate significant regional and type heterogeneity in the changes in the carbon emission performance index of RBCs. Finally, based on the analysis results, implications are proposed to enhance the carbon emission performance of RBCs of different types, as well as at the national and regional levels.
