Earth is still more hospitable in the case of your giant asteroid. Those in nuclear submarines and bunkers will survive unless they're very close to the epicenter. When they emerge, they'll find temperatures and atmosphere which are much more hospitable than on Mars. The survivors will also be able to scavenge abundant refined metals from the dead for rebuilding.

We can also start improving these facilities today, if we care about the survival of homo sapiens. Even out the gender ratio at Cheyenne mountain, give it a small nuclear reactor, a hydroponic farm, and a seed bank and we can be reasonably confident in it weathering anything but a very near miss.

As far as we're aware of, the crust of Mars is even more sterile.

I'm pretty sure humanity currently possesses the knowledge and resources to build multiple underground shelters around the Earth (as seen in Hollywood movies) that can sustain a population of at least one million indefinitely. Food can be grown with artificial lighting. Air and water can be brought in from outside, purified and recycled. If you need anything else, send robots (or people in protective suits) to scavenge the surface. The only thing we lack is political will.