For a run, tightly stretched and fastened chicken wire will leave holes big enough for a raccoon's hands to reach through, this is never good for your chooks, they will be killed and left inside the run. For a roof on a run chicken wire is acceptable if you can support it well enough that a heavy critter (raccoon, opossum) won't fall through. If you have enough posts around your run, you can use heavy wire to create a lattice of wires and then put chicken wire over those.
We live in the country, surrounded by woods, we have fox, raccoon, opossum, wild dogs, coyotes and cats as main predators. Our set up uses chicken wire as one layer, covering from top to bottom. Over that we have used 6' tall, 1/2" square hardware cloth that goes up 4' with the other 2' laid out away from the run and stapled to the ground, this is covered with dirt and grass so it is hidden from view. We may end up adding a single hot wire on the outside but so far we have not had any animals try to climb this fencing.
To keep air predators out we have strung multiple runs of wire, crossing so there is no empty space more than one square foot, this keeps hawks, eagles and owls from getting in. The chooks are put up in their coop every night before dark and the doors locked. For our situation this setup is working very well.
I think you have to assess all the needs you have before making decisions on what to use and how best to use it.
If we find out we need extra protection, then I will put up a new fence of 2" x 4" wire fencing inside what is already up on the outside of our posts.