Which unit is most suitable in comparing needed light intensity for night reading on the Moon, vs on Earth?
Readability requires taking into account the sensitivity of the human eye to various wavelength. This is called Illuminance.
Physics knows Lumen (flux weighed by human perceptibility) and Lux (flux per unit area weighed by human perceptibility).
Quoting that, different light sources have roughly these values:
Source             Lux
Full daylight   10,000
Overcast day     1,000
Very dark day      100
Twilight            10
Deep twilight        1
Full moon            0.1
Quarter moon         0.01
Starlight            0.001