Why do Green LEDs throw farther than White LEDs?

Nope.

The shorter the wavelength, the more the energy that light carries.

In a white LED (should it be more or less perfectly white), a considerable portion of light is emitted at those wavelengths, where human eye is less sensitive. If a LED emits its most light near the wavelength where human vision is most sensitive, then it can be more efficient.

Use the left function for the scotopic vision (where it is not enough light to get response from the color sensitive cells in the retina), and the right function for the photopic vision (color is perceived).