In the right Picture the albedo (relative brightness) is not original. "the brightness of the Moon is increased relative to that of the Earth" . But even then the earth looks much brighter than the moon.
On the page Looking Over The Limb, Posted by Mark Robinson on December 18, 2015 12:53 UTC on the website LROC - The Lunar Reconnaissance Orbiter Camera is a detailed description, how the image was vomposed from the LROC data.
From the folloing original scan we can measure the relative brightness of earth and moon e.g. with photoshop. The result is: Earth = 100%, Moon = 30.8%. So the earth is 3 times brighter then the moon.
The following images are not photoshoped to enhance color or contrast. They show the original brightness between Earth and Moon.