I will admit I am building out chicken run with 1" poultry wire (not the super flimsy 2" chicken wire they sell here)
We have had chickens since 1965 at this lot, I think we have a good idea what kind of critters we will attract.
It will be a small run (6x8), I scored some 1/2" hardware cloth, so that will get used around the lower 2' of the run (hope I have enough or I will have to find some more) I will even bend a foot or so and use as an apron around the run. 12x12 pavers will surround the whole run.
In the past we had chainlink and the flimsy chicken wire. It was a bad job of pulling the chainlink, all scrounged up stuff my dad had brought home over the years. We lost a couple of chickens with that set up too.
Of course I know the big chicken killer around her place for the past few years, my dog...sigh He used the people door to get in. He is 8 now and a 24" kennel panel will keep him in, so I feel good about only going up 24" with the hardware cloth
I mostly deal with that predator by using a leash and not letting him on the chicken side of the fence.
In the past we did loose a lot to critters in the night, but that was before I rebuilt the old run with the chainlink and they did not have a proper locking coop to be safe in at night. Critters would find any crack we left and get in. We had a tree growing out of the thing and it was usually the entry point, or the people door that never fit right or the chickens themselves taking dust baths and leaving critter sized holes. Raccoons and opossums.
We now have a nice and secure coop to lock them in at night, the run is just for when it is rainy or when we need them contained, thus I am less worried about using poultry wire. They free range every day otherwise. We did have a young hawk take a swoop at them this winter, first time I can remember. We have cut down a LOT of trees so the hawk almost had room to swoop-he nearly hit my mom instead and that was the last time he tried it. We do have a lot of trees for them to hide under, chairs, tables, even branches they can take cover under. Our neighborhood has also changed, more and more upscale homes, less open space. We have also cleaned out our lot so there are few hiding spots for critters to take cover.
Because our chickens will be secure at night and free range in the day on a fenced property, I am willing to take the of risk using poultry wire.
I would probably feel different if I was new to chickens or knew I had more aggressive predators.