First off let me say the following reply is merely my "interpretation" of what I've experienced and read and learned while in this hobby.
To my knowledge the "K" rating does not affect the actual temperature (physical temp) of the bulb, fixture or the tank.
the "K" rating is sometimes called "Bulb Temp" but that's not what it means... at least not to us. What it means is the actual color a black body radiator will give off at the precise temp. The lower the "K" the more yellow (at least in our talks here) and the higher the more blue or even white (again just for our talks).
10K is considered a decent compromise between growth and color. 6500K is considered the best GROWTH (at least in the broadest range of coral) but it's very yellow and for some even bordering a reddish hue. When you get above 10K you start seeing more blues and when you get up into the 14K and 20K you'll see a LOT of blues. I personally LOVE 14K and higher. Keep in mind that a 14K from one bulb manufacturer may look significantly different than from another company.
I personally have started using and LOVE the new AquaMaxx brand bulbs. I'm running 14K and they do appear to be similar in color (that which is perceived by my eyes) to 20K from other companies. If I were buying new bulbs right now I would again buy 14K AquaMaxx bulbs.
For a short "primer" on Kelvin in terms of "Color" try this link and look under the section "Color Temperature".
Kelvin - Wikipedia, the free encyclopedia