I planted both and the baby tears ate the Corsican mint. It depends on the type of sun- coastal or inland, December or August. Mine creeps out to fill the shady area in the winter and dies back to roots for the summer, but then it springs back with the rain and cool again.
Renee

In my experience Corsican mint needs much less water than baby's tears and can actually tolerate fun sun. I think in the appropriate conditions (lots of shade and water) baby's tears will tend to dominate Corsican mint. I find Coriscan mint a bit more unreliable however. It doesn't seem to form a nice solid ground-cover, but instead wanders here and there, setting up shop on a whim. It is so deliciously fragrant, however; perhaps the most intense mint of any plant.

-Brett