The chances that Earth & Mars shared life is very remote.
First of all, the microbes would need to survive asteroidal impact.
Second, they must be in a piece that gets to the other planet.
Third, it must get there before it is sterilized by cosmic rays.
When one considers how difficult even rafting a few hundred kilometers over open ocean on driftwood is, and how the oceans have effectively separated life into different zones, I would say that it would be a VERY long shot for any interplanetary exchange of life to happen. Look at Wallace's Line that separates Australia from Asia and acts as an effective barrier for the transmission of life.
David F Mayer
