I guess this question depends on what your are capturing. We do know that early morning and late afternoon can lead to some great images, especially for landscape pictures. Case in point this image was captured as the Fall sun was setting at a wildlife sanctuary in Connecticut.
Also, many people think that if it's not sunny out, we are not going to capture some great images. However, grey days can eliminate harsh shadows and the sunlight from impacting the color of our subjects. Using photo editing software to enhance colors can lead to a dramatic color contrast against a grey sky.
In some cases, sunlight can also lead to interesting effects or desired outcomes in the images we capture. One can think of the rays of sunlight penetrating through trees to illuminate a subject located underneath the canopy.
So is there a better time to take pictures? It really does depend on what you are capturing, creating the impact and effect you want.