Count me lucky, or somewhat vigilant, but I've free ranged my birds (to just mean backyard, whole yard, not the whole neighborhood) and not a single predator loss. That is, not counting the baby duck hatchlings/eggs that a king snake must've gotten. We had built our first run/coop, and decided against putting hardware cloth under the entire interior of the run, just had an apron. I have crows where I am. I have a lot of deciduous trees in the area the birds are confined to, so I'd think it'd be hard for a raptor to make a swoop at my birds. But, it's a trade off, you have to be able to accept losses. I enjoy seeing my birds out enjoying the yard. I'd love to see some larger predator proof run/coop setups though.
Oh, and in that first setup, we had about 80 x 100 under bird netting to keep out the aerial predators. I lost a whole garden (never sprouted except for a few) to mice who had nested in the garden bed, same timeframe as the king snake. So in keeping any predator out, we have to think about the food chain--another tradeoff for us chicken owners!