There are some minor differences between the towels of different colors. First is that the dye in darker color towels is heavier, and makes the towels feel less soft. So a black, dark red, or dark green towel will be a bit more rough than a white, light blue or yellow towel. Second is that some of the darker colors like black and red will bleed in the wash. Third is that lighter colors will stain and show the dirt they have picked up (sometimes this is desirable and sometimes it is not).
Many cleaning professionals like to color code their microfiber cleaning cloths based upon their usage. Auto Detailers will use one color for paint, one for interiors, and another for wheels. Hospitals and housekeepers will use one microfiber cleaning towel for bathrooms, another for surfaces, and another for spills.