White mesh has more light refraction than a dyed mesh. In other words light will scatter on a white mesh causing a less resolute image. White is usually used in lower mesh counts, up to 155 count, which typically are used, for spot color work or larger text.
Yellow or dyed mesh, on the other hand, has very little light refraction. In other words you get a much truer image, resulting in a more defined edge and a crisper print. On counts above 155 you would typically use a dyed mesh.
One thing to keep in mind, is that a dyed mesh will have a bit longer exposure time than a white mesh, about 15-20%. Otherwise, they are handled the same way, no matter the color.