[Enchilada]

The colours are matched to the amount of methane in the planetary atmosphere

Methane happens to absorbs much of the faint red-light received from the Sun, which makes Neptune have the richer blue colour.

Uranus has a composition is approximately 82.5% Hydrogen, 15.2% Helium and 2.6% methane.

Neptune is 84% Hydrogen and 15% Helium, with the Methane content being the remaining about 3%.

Uranus appears greener because of the slightly higher temperature of the atmosphere, even though it has less methane. Neptune atmosphere probably also has some more of the colder icy methane.

As I understand it, the chemistry that is happening is not entirely understood, though I remember reading some inconclusive technical paper on experiments in the laboratory.

Regardless, the complex chemistry in the upper atmospheres of these outer planets is likely making the slight colour differences - 'greener' with Neptune'. Combined with the methane being the main contributor of the 'blueness' seen with both planets.