Fantastic work there!
The overcast sky of the first image suits the mood of the image, but it’s almost entirely black and white. most of the objects in the scene are basically grey, so without any colour in the lighting … it looks like a photo that has been filtered to remove colour from most areas.
The sunny day, with the blue of the sky and the yellow of the sun, creates some colour even if the materials are all mid grey.
The easiest way to fix this would be to find another HDRI that is still overcast, but with some colour to it.
