It ultimately comes down to durability. The sword is clearly cooler, but it will break one day. The perfect stone is forever.

Personal preference.

If you take a stick and I take a rock, soon I’ll have both a stick and a rock.

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.

Stick.

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.

If both take the stick, get a camera.

What about paper?