The benefits of selecting different colors of white come from being able to better select a light color that matches your needs. See the chart below (U.S. EPA - ENERGY STAR®).
How do you know which color you are buying?
Unless they state otherwise, the standard color for today's CFLs is the warmer soft white because these are closest in color to the incandescent bulbs they are replacing.
Many consumers feel the standard warm light is too dim. As we age our eyes need more light for reading and performing tasks. If you find yourself sitting near a window to get the best reading light, then try a bulb labeled "natural or daylight." They are designed to deliver a more vibrant blue-white color that can provide light that is excellent for reading tasks. Take it one step further and increase the wattage equivalent to 75 watts - this only uses 18 watts and will still use much less energy than the dim incandescent you are replacing.
Likewise if you enjoy hobbies or perform work that requires you to see details, try the "cool white or bright white" labeled bulbs.
So when you plan to make your CFL purchases, keep the shades of white light in mind and purchase a color that best suits your home, application or mood.
The science of color
Color in lighting is measured on the Kelvin scale (abbreviated "K") and can be found on CFL packaging or the bulb base itself. The lower the number, the closer the color is to the soft yellow of a candle flame. The higher the number, the closer it is to the brightness of the sun, resulting in "cooler, bluer" shades of light.
Variations and inconsistencies in color still exist among manufacturers. Some vendors do not include the Kelvin value on the package, but this is beginning to change.