The Minium Stone appears to have durability, though I'm not sure exactly what wears it down. Possibly the crafting trades. The Philosopher Stone cannot be crafted, currently, but I don't believe it has durability (I could be wrong), and it can enlarge the area that it can transmute in the world. For example, the Minium Stone can only turn one Dirt block into Sand at a time. The Philosopher Stone can turn a small area at a time.