Definitely the stick. A perfect rock is only good once, which is when you throw it. A stick is good for decades. My dad has a stick I found 36 years ago and still uses it. Nobody uses a rock for that long.
What is stopping you from picking up the rock after throwing it? Let me tell you, I still have a little pebble I found by a river some 20 years ago and it's not even a particularly cool looking rock or anything. If I had a perfect rock you better bet I'd keep it forever.