A mixture of both. My chickens have access to a coop to roost and lay, as well their run is 1/2 covered with that wavy tin stuff and a roost outside underneath that. I integrated some cuckoo marans with my 4 week older EE's and the cuckoo's prefer to sleep outside, probably because the EE's are racist...
I like some cover on my run outside because the feed and water are hung from the rafters and this keeps the food and the birds dry if they prefer to stay outside during a rain. Also, should it snow, there will be an area of the run that won't have six inches of that for them to wade through just to be outside.