So, would it be a fair statement to say this. "A 15w/10,000k bulb would give off more of the full light spectrum than a 40w/6,500k bulb" ?
No, not at all. "Full light spectrum" is a variable,depending upon the light source. For example, the spectrum of an incandescent bulb is markedly different from that of a metal halide. The peak output of a light source is indicated by the Kelvin temperature of the source. A higher Kelvin temperature is "bluer" than a lower Kelvin temperature, which tends to be more yellow or red. Just for reference, the sun emits at 6,500K, measured at the top of the atmosphere.
For terrestrial growth, professionals tend to use higher Kelvin temperatures for initial growth, while using lower temperature sources for flowering; so, the "correct" temperature not only varies by plant, but by growth phase.
It's not often a good idea to emulate the solar 6,500K with your aquatic lighting. Our eyes are adapted to increased sensitivity to "warmer" parts of the spectrum (reds/yellows), and a 6,500K output will appear "unnaturally" blue to the eye. Ironically, a "cooler" (i.e., bluer) light may be better for plant growth. The reason for this is that the reds and yellows are absorbed by water more quickly than blues. So, a lamp with a higher blue output (e.g., 10,000K) will deliver more light to the plants in deeper water. For the same reason, aquatic plants have evolved to use those colors for photosynthesis to a greater degree than their terrestrial counterparts.
I use a fixture that employs SunPaq bulbs (Current USA fixture). Part of the bulb delivers 10,000K radiation, while part of it concentrates its output at 4,600 Angstroms, which corresponds to a blue-violet color.