Effects of atmospheric gases on colour of aurora
There is good information at Glowing Gases - Aurorae 

There are many factors that need to be considered.  

Once an atom or molecule is excited, it can lose the energy by collision or by emission of light.  

The longer the lifetime of the excited state, the higher the altitude is required to make radiation vs. collision the way energy is lost.

The atomic oxygen transition with green light has a lifetime of about 1 second, while the transition for red light is 110 seconds, so a higher altitude is required for the red transition to become significant. 

For molecular nitrogen, radiative lifetime is only $4 \times 10^{-8}$ seconds according to Electronically excited molecular nitrogen and molecular oxygen in
the high-latitude upper atmosphere Ann. Geophys., 26, 1159–1169, 2008

Also, human eyes are more sensitive to green light than red light.