There's no climate scenario in which Mars is more habitable than Earth. Even if a Texas-sized asteroid crashed into Earth, Earth would still be more habitable than Mars.
I think this is true in almost any scenario. A Mars base is a second chance in the same way that a single potted orchid, suspended by a gossamer thread over a roiling vat of acid is a second chance for your lawn. If you humanity completely wiped itself out on easy mode, it will not last long on Mars after that.