This
video is the best answer I've found on the topic. It suggests that the atmosphere is pretty transparent to light in the visible spectrum (the light it blocks is mostly UV, etc.) Something like 98% of visible light gets through assuming it's travelling through pure atmosphere (i.e. not much water vapour or air-borne dust in the way).
Probably the difference between the faintness of stars you could see in space versus on Earth would be less than the differences you'd find between different people. It's plausible that you might have one person in the Atacama desert and another on the Moon, and still find that the person in the Atacama desert can pick out fainter stars, just because their vision is better suited. What would be different is that the stars on the moon would be crisper, and wouldn't twinkle, due to the lack of turbulent atmosphere.
I could be wrong though. The internet is not a good place to check facts, and I'm struggling to validate that 98% figure.