Color balance is as much about what "looks" right than about meeting some idealised concept of "correct".

Without examples of what you are talking about any answer is pure speculation but I can list a few things that may be different between sunny and overcast conditions.

• Direct vs diffuse lighting. Sunny days have a high contrast between parts of the subject lit by the sun and parts in the shade, whereas overcast days are by nature diffuse, and not necessarily in a flattering way because it's still light that's coming predominantly from above.

• Effect of blue sky (atmosphere). On a sunny day the blue sky adds a blue hue overall, and particularly to shadows - that is, all reflected light from the sky is more blue, and this is more noticeable in shadows because it's not competing with direct light from the sun - whereas direct light from the sun is warmer, giving a contrast. On overcast days there isn't this same balance and the hue of all light will be more uniform.

• Dynamic effect of clouds. The varying types and thicknesses of clouds and the fact that they move relatively quickly can mean that on a cloudy day, the exposure and color balance changes throughout the length of a shoot, making it hard to get consistency between shots both in exposure and in color balance.