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The OpenCV circle grid detector implementation uses subpixel precision, so I doubt that would be the reason for any quality difference when compared to the checkerboard detection implementation. Without knowing anything further about your experiment setup, its impossible to say why you got such results. In my experience I get the exact opposite result, circular board patterns give me a good 50% lower RMS value.
As an aside not, I would be careful about using the RMS score to judge the quality of your calibration. Camera calibration and especially stereo calibration is highly sensitive to the quality of your input and because of this it is critical that you take calibration images with high variety of poses, and for stereo that image pairs are correctly synchronized. The camera calibration implementation in ROS has some good metrics for evaluating the quality of the input calibration images, check it out here.
