I have heavy duty tarps for a roof on my run. Even with the silver side down, it's kind of dark and gloomy in there. So we're going to go with clear polycarbonate for a more permanent roof.To me, part-open, part-sheltered seems like an ideal setup.
I figure that chickens know how to be chickens better than I know how to be a chicken so I like to offer them choices -- sun or shade, weather or shelter, inside or outside ....
The sides are all open to the breeze, and there is some shade available. In the sunniest months, I can put the tarp over the polycarb to add to the shade.
I plan to enlarge the run too, and it will have just HC for cover. Then, as @3KillerBs mentioned, the chickens can choose where they want to be.