Emission spectrum from the sun peaks at under 500nm corresponding to >5800K. Emission spectrum from the moon peaks at 600nm, corresponding to <4100K. Moonlight is objectively colder and therefore gives less energy. Reflection does not necessarily preserve spectral characteristics.
https://nvlpubs.nist.gov/nistpubs/jres/118/jres.118.020.pdf
https://earth.gsfc.nasa.gov/climate/projects/solar-irradiance/science