Depending on the pigment size and other additions, the melting temperature and crystalline/amorphous structure of prints vary vastly.
Titanium white, the most common white pigment in the industry, needs to be applied in large doses to get a good coloration. This means that the brighter the white, the larger the percentage volume of the item is made up of the pockets in the polymer structure that contains the pigment, resulting in a more brittle structure.
Carbon black on the other hand is one of the most effective black pigments known to man and can be used very sparingly. It also is an almost perfect UV-absorber, making such prints heat up much more than those of other colors. It also can protect the polymer itself from aging if the polymer chains degrade under UV light. ABS for example does undergo degradation in UV light.
Some polymers also contain some kind of filler to adjust melting temperatures:
I have encountered PLA spools from two different manufacturers in the almost exact same color before printing. However, the one brand printed well already at 190 °C, the other required 200 °C to print decently. The two filaments also looked vastly different after printing: the hotter printing one showed a much higher gloss after printing, which hints that they had a quite different makeup besides the PLA - either something in the one was making melting easier but reduced gloss or something that increased gloss also rose the melting point.
Another thing I found was, that the clear PLA I got from china once printed best at 110 % flow of other PLAs in combination with only 185 °C, making me believe that something in the treatment to achieve the translucent filament also results in altering the flow behavior.