Op: It depends on how busy the campground is, in my opinion. If it is a busy one, with kids dogs and bikes going by constantly, then I think a leash is best.
Especially, if your dog is like mine, and he will take off to the end of the lead if a dog walks by. That can really scare the heck out of someone. They see the dog, not the rope he is tied too. And if a say national forest, pretty empty then we will use a rope.
Yes I know, I am a bad fur kid parent, but him running at other dogs is something we have never been able to break him of. I am about 99% sure all he wants to do is play, but any dog including mine will bite.
So out of respect to other campers, who can be frightened by a big dog running at them, and not see he is indeed on a rope, I feel a leash is best, for a busy place.