The earth’s surface reflects almost 3 times as much sunlight as the moon does, making the moon look dark by comparison. But we never see a direct comparison between the earth and moon, except from space. Per unit of area, that is approx. true.
But I suspect that the luminosities of the Earth and Moon in this image were, in any event, corrected. I namely highly doubt that the part of the Moon visible in this image was in sunlight at that time.
Regards,
Like the earth, the sunlit part of the moon in this photo is near the top, which you are looking at. The brightness has not been corrected at all except to adjust the exposure so as not to overexpose the earth. Here are some pictures of the Earth-moon system as taken by the Cassini probe in 2013:
As you can see, the moon is quite dark when compared to the Earth.