Coral growth vs. coloration

I'm not sure I'd say lower K necessarily gives better growth on any given coral. What it does is provide a greater range of spectrum, therefore you will have the optimal spectrum for a wider range of corals, although possibly less of it in some cases. This is likely to be especially true for deeper water corals, which are more adapted to bluer spectrum. This is probably ok in most cases though, as we often give, especially deepwater corals, more light than they can utilize anyways. Maybe it's actually better to keep similar corals in separate systems with specifically optimized light. It's probably easier to just use wide spectrum though.

Also, K really dosn't say anything. It is just a marketing designation. No corals are adapted to red light, it is filtered out within the first few meters of water. Some low K bulbs will have red, others of the same rating won't. There is some evidence red may be detrimental to growth actually, so, this is one valid reason to compare bulbs based on spectral plots rather than K ratings.

As to coloration. I'm not sure if your referring to pigmentation, or perceived coloration? Not much is known about pigmentation and why it exists. Some people say it is a sunscreen against UV or High Energy Visible (HEV) light. However, other research seems to show that these sunscreen pigments are actually clear. If not to protect against harmful light, another theory is that it optimizes the internal light spectrum for hosted zooxanthellae. Regardless, I haven't seen any data showing that the pigmentation changes in response to spectrum. It may, and that would be interesting to document though. It is difficult to quantify though, as the perceived coloration will be directly effected by the spectrum of light and there may be other factors such as zoox density, which will likely change based on the spectrum provided. I think this is more the case, because when I have run systems with lower K, and moved the corals to higher K, the coloration usually becomes apparent immediately.