I can't keep chickens yet, myself, but from what I've read here, you'd want to have the top of the run covered to keep out predators like hawks, raccoons and opossums. Since your run surrounds your coop, you wouldn't be able to get to the coop unless it was high enough for you to stand in. So why not go with 6' privacy fencing around the run and just do whatever kind of coop you like? With fencing that tall the neighbors would only see the fencing.