So, the difference between 10K, 12K, 14K, and 20K is basically the ratio of the amount of short wavelength (violet to blue) light that's emitted to other wavelengths. The higher the Kelvin (K), the more "blue" the light will appear. For the growth of zooxanthellae in corals, they definitely need light in the blue spectrum, but they also require a good amount from other wavelengths too (like red). In this case, 10K (a more whitish light) is actually the best choice, although some deeper water corals are more accustomed to using more blue light. So, 14K-20K would be good choices for them. However, we also have to factor in aesthetics. Things in the aquaria just look better when you have them under bluish light, so we add more blue light to provide that look. You can find out more about light output from various common bulbs in Sanjay's Lighting Guide on the home page here; it's quite useful and detailed.
My light happened to be sold with 10K, 14K, and 20K. I'm using the 14K for my tank because I think it just looks the best of the three and because I have no actinics but still want the bluish tinge. The 10K looks much more yellow in comparison, and the 20K is closer to being entirely blue.
