I just can't imagine mining the moon being in any way shape or form easier than mining the earth. The list of workplace hazards would be impressive. I imagine we're talking surface mines to keep the logistics manageable, but then:
1. How do you get astrominers there and back safely and on a regular basis whilst still keeping costs down?
2. What would it cost to keep your astrominers well fed and rested in a comfortable environment (warm, enough water, entertainment, etc)
3. How much more in bonuses (danger of hazard, long way from home, etc) do you even have to pay an astrominer vs a terraminer?
4. Most mines have some form of processing on site, e.g. break down rocks and sift through shit. How do you get those massive machines up there on the cheap and service them frequently on the cheap? Do we even have the machines that can work in those conditions?
5. Gravity is weak on the moon, I can imagine rocks of considerable mass flying or tumbling about being an issue. Sifting doesn't work as it does on earth without normal gravity and abundant water.
6. etc. etc. etc.?
I mean I think it'd be cool if we could pull it off as a civilisation but I just can't imagine how out there in scope and complexity moon mining would be.
But I think mining asteroids will be easier than mining the moon. Because on asteroids, everything is right at the surface. There's an asteroid that seems to be just the nickel-iron core of a former planet. That's more nickel and iron than you could ever hope to mine on Earth, and there's no planet around it.
Mining the earth is of course the easiest, because we're already there and there's no space travel or vacuum involved. But it's also very destructive, and once you tackle the space travel and zero-g mining issues, I think asteroid mining is going to be way more profitable. As well as saving our planet.
I can imagine dragging smaller asteroids and letting them "drop" into earth (e.g. attach massive parachutes and then guide them to land on some mining site. Totally sci-fi but I still find it less so than the moon. The reason I don't imagine robots mining the moon is that minerals, as you say, are not readily on the surface, nor is the moon mainly made up of a specific mineral.
I once heard that the one thing we might mine on the moon is He3, once/if we get to that level of fusion power. There's apparently a lot of it, and it's right at the surface.
But the advantage of asteroids is that everything is at the surface.
