One difference is gravitational pull; martian gravity is ~2x lunar gravity, which makes the solar wind an even larger danger to any atmosphere you would generat

One difference is gravitational pull; martian gravity is ~2x lunar gravity, which makes the solar wind an even larger danger to any atmosphere you would generate. The distances from the moon's surface at which atmosphere could be stripped away would be proportionally shorter. In either case, the technological breakthroughs we would need in order to actually generate a useful atmosphere are large enough that I would be very excited to just see the byproducts of such breakthroughs.