Asteroids don't cause extinctions by coming in and blowing everything to smithereens. Rather, the ejecta causes firestorms, and an impact winter can wreck the biosphere and prevent sunlight from reaching the surface. But even during the worst of this, Earth will remain more hospitable than Mars.
There's no reason for a self-sufficient (nuclear?) underground or underwater habitat to notice global firestorms or impact winters. They would notice a direct hit, but you can hedge against that by building them in multiples around the globe.
It's a lot harder to build a self-sustaining colony on the moon than on Mars. Mars is rich in carbon, oxygen, hydrogen, nitrogen. The moon is not.