[bjrnjs]

"To wipe out all humanity with one impact, you would need to hit the Earth with something in a slightly larger class - say, the Moon"

No, if an object as large as the moon hit the earth - the earth might even be destroyed (but probably not). To wipe out humanity a body of the size between 10-100 miles in diameter would probably suffice. Fortunately near-earth orbits with a body of that size is rare.

[samastur]

What I would like to know is what kind of event do you imagine happening (beside practically completely obliterating Earth) that would make Mars more hospitable than post-apocalypse Earth?

I'd imagine polluted water and air with still some flora and fauna would still be better than none of those things.