The stick is superior, but the question is which one you take. Take the rock. Use the stick, then leave it in a conspicuous place for the next person to find and enjoy, to maximize the stick value.
In a duel between 2 people, if both take the rock, both will be hit by rocks. If 1 person has the stick and the other has the rock, one person has a chance, however small, to deflect the rock and hit the unarmed assailant.