what is the relevance of that blue spike? Incandescent spectrum looks much more linear (http://housecraft.ca/wp-content/uploads/2012/09/spectral_res...), but appears to maybe emit more (just judging by eye) aggregate blue energy than the warm white LED.
Then again intensity towards blue-green still seems much higher in the LED, and maybe that matters more?
I haven't managed to find an LED warm/soft bulb that actually has a spectrum like in the chart you linked.
The spectrum I linked above is from http://www.designingwithleds.com/measuring-light-quality-phi... -- it's for a Cree Soft White bulb. There's a bunch more area under the curve over the range that seems to matter for that bulb than for the incandescent one (although incandescent bulbs might not be great at night either...)
Green light does alter circadian rhythms as well, although not as strongly as blue (peak responsivity seems to be ~460-480nm). The actual circadian-wavelength-responsivity curve doesn't seem to be well mapped out, as far as I can tell.
I would suppose that intensity is as or more important than exact wavelength (within the violet-to-green range), given the increasing intensity of the rising sun is the origin of our circadian-rhythm adaptation.
Then again intensity towards blue-green still seems much higher in the LED, and maybe that matters more?