Sandy Beach identified Albedo as the key measure - and they were spot on for that providing the most scientific approach to determine how much moonlight a specific moon would give off.
Albedo is rated on a scale from 0 - 1 in decimal points. It also generally refers to radiation in the visible spectrum - An interesting concept COULD be if the Albedo was different for different species - therefore giving humans one amount of moonlight and some non-humans a completely different amount of moonlight - eg if their visible spectrum ran much more towards the Infrared or ultraviolet spectrum...
Here is a list of some materials you could potentially "make" an airless moon out of - with their respective Albedo (in the Human visible spectrum):
- Desert sand (grains of silica), 0.4
- magnesium oxide - 0.96 [D]
- matte aluminum - 0.55-0.6 [D-S]
- matte silver - 0.7 [D-S]
- polished aluminum - 0.65-0.75 (S)
- polished silver - 0.88-0.93 (S)
- yellow clay - 0.16 [D]
And here is a list of things you could potentially "make" a moon with atmosphere out of - with their respective Albedo (in the Human visible spectrum):
- Fresh snow, 0.8 - 0.9
- Ocean ice, 0.5 - 0.7
- melting snow (clean) - 0.6-0.62 [M]
- Ice (Sea) 0.3 - 0.45
- Bare soil, 0.17
- black soil (dry) - 0.07-0.08 [D]
- black soil (wet) - 0.02-0.05 [D-S]
- Conifer Forest, 0.08 - 0.15
- autumn foliage - 0.15-0.3 [D-S]
- Deciduous trees, 0.15 - 0.18
- Green grass, 0.25
- Sand 0.15 - 0.45
- tar & gravel - 0.33
- Tundra 0.2
- white dry sand - 0.24-0.32 [D]
- white wet sand - 0,11-0.2 [D]
The letters in brackets refer to:
- D diffuse
- S specular
- M mixed
I found this list collected in this post here:
which is in a forum dedicated to the rendering software Corona:
Albedo is reasonably important in that kind of software so it would make sense someone there would be interested in collecting lists of Albedo of a wide range of materials.
I might not have got the split between airless and moons with atmosphere materials quite right - I suspect clay would change it's albedo if all moisture bled out of it for example.
This would give you a bit of a start on some reasonable scientific approaches. I don't have ANY idea how you would go about getting a list of Albedo for wavelengths outside the Human visible spectrum though... So my list wouldn't really help on my earlier interesting concept :)
To give an example of a moon that would give off a large (Read insane amount) of reflected sunlight would be if it was made largely out of Magnesium Oxide (Which is listed as having an Albedo of 0.96) This means that 96% of all light hitting it is reflected back out.