I may have just been really lucky, but I have never lost a chicken to a predator (other than the dogs when one bird escaped).
I've had my birds for 7 years, half the run is 2x4 welded wire, the other half is chicken wire (we ran out half way through the build). The coop has chicken wire on the inside (big shed, we leave the doors open all summer long), and there is a regular screened window.
My coop is in the woods, and I know we have possums and racoons. That being said, I have never had an attack by either one. It may be because of the goat's pen is right next to the coop, or the fact that we have cat food outside 24/7. We have had possums and racoons eat the cat food, which it only about 10 feet from the chicken coop. They may just decide to go for the easier meal. I would not feel too horrible if we lost our bird to a predator, so I decided not to spend a ton of money on the run.