I started with uncovered (actually I started totally free ranging, but had to pressure wash all horizontal surfaces every week). Birds kept getting out. Turns out barred rocks have no trouble flying up 6 feet. Not such a big deal but we are getting ready to go away for a few days and I don't really want them out, so I get some bird netting from the HD garden department and covered the entire run (15 x 40 feet). Finally, only one was getting out. She was just skinny enough she could squeeze through the welded wire where one of the welds had broken. I put a layer of chicken wire over the bottom of the fence and now they are all in for a week.
Just finished mine and covered it before letting the girls out. Within no time, the barn cats were walking across the top looking for a way in. Sure glad I covered it.
we are covering ours-we have chicken hawks flying above all the time-We are the only ones with chickens in a 30 mile raidus-I know they want my babies! Not too nervous about my grown BO's but the chicks are 10 weeks old and easy pickings-and My puppy worries me too-he's almost 10 lbs now so I feel a little less scared-when he hits 15-20 Ill let him terrorize the hawks and crows!