In this study, 28 climate models from the fifth phase of the Coupled Model Intercomparison Project (CMIP5) and 32 models from the sixth phase (CMIP6) have been evaluated for their ability to simulate large‐scale atmospheric circulations (using rainfall, wind fields, geopotential height, temperature, and moisture flux convergence) for the summer monsoon in Southeast Asia. Using a multi‐criteria decision making technique, models have been ranked based on 25 metrics which compare their performances with observation data. Results indicate a better representation of annual rainfall cycles as well as spatial pattern by CMIP6 models compared to CMIP5. Though majority of the models from both CMIPs show late onset and early retreat of the rainy season, CMIP6 GCMs simulate the onset, retreat, and the length of the rainy season closer to the observation. Large‐scale circulation patterns evaluated using spatial correlation and root mean square error (RMSE) show improvements in CMIP6 across all metrics, especially for the moisture flux convergence. Performances for large‐scale circulation are generally reflected in rainfall simulation; however, few models showed that better simulations of rainfall do not exclusively depend on their performance for large‐scale variables. Overall, CMIP6 models are found to be superior to CMIP5 models in simulating rainfall and large‐scale circulation, which is likely attributable to CMIP6 model's higher spatial resolutions, increased number of vertical levels, improved atmospheric and land surface parameterization, etc. Finally, subsets of optimal models from CMIP5 and CMIP6 that proved to be better at representing the summer monsoons in the study area are identified. These models are recommended to develop robust future projections that can be used for climate change impact and adaptation studies.