The increase in electric vehicle (EV) penetration has triggered a surge in demand for battery charging and swapping infrastructure. However, in diverse urban regions, an unbalanced allocation of charging stations (CSs) and battery swapping stations (BSSs) can lead to inefficient resource utilization and diminished revenue for these facilities. Therefore, it is urgent to set up a system of operational and economic indexes to evaluate the proportional planning of CSs and BSSs. The traditional weighting method of the index system cannot accurately describe the relationship between the indexes. As a result, an evaluation method of CS and BSS operational economy based on dynamic weighting indexes is proposed. Firstly, from the perspectives of EV owners, CSs, BSSs, power grid, traffic, and environment, a social and economic index system of CSs and BSSs is established, and quantifiable indexes related to the operational economy are extracted. Then, the copula entropy (CE) is used to improve the CRITIC objective weighting method, reflect the correlation between indexes, and align it with the objective law. The selected indexes are weighted by the subjective and objective combination weighting method. Finally, the simulation is conducted based on the practical data of the urban power grid in China. The rationality of the proposed operation economic indexes and the effectiveness of the improved weighting method are verified.