What you're observing is a quirk of human biology. Our eyes overemphasize certain ranges of color, particularly midrange on the visible spectrum:
"Full Spectrum" bulbs usually have a strong emission band in the yellow-green spectrum where, as you can see from the above picture, there is high absorption and a greater deal of overlap. "Plant Grow" bulbs tend to have strong emissions in the red spectrum, where as you can see there is little overlap and less absorption. Plants, on the other hand, "see" light like this:
Notice the increased absorption in the red range? This means that bulbs that have stronger emissions in the red range are "brighter" to the plant. There is a similar effect in the blue region as well.
As an aside, this is one of the reasons that I think people saying that 6700K bulbs are best for planted tanks. The color that 6700K corresponds to is in the yellow-green area where plants are essentially "blind". It's actually the non-6700K emissions of 6700K bulbs that plants can actually use.