The one that I'm currently building (about halfway through that process now) will be covered for shade... we've had uncovered runs in the past and a run covered in netting and neither were much of a deterrent to predators (the netting doesn't take much to deteriorate to the point of not being functional). We lost so many birds to hawks and other predators over the years... I would NEVER use netting again, it was basically a huge headache and wasn't really that useful, and I'd shy away from having a run that wasn't covered as well. The design of our prior coop/run didn't make it possible to cover it without basically rebuilding the entire thing, which I was never ready to commit to doing (the coop had many other issues too, which is why I'm building a new one).
The chicken tractor that I built to "solve" that problem was covered in 1x1 cage wire and eventually we threw a tarp over it for shade... it still wasn't/isn't completely predator proof though.