My first criteria when positioning a coop/run is how well it drains. If it drains well it should stay dry enough to not cause problems. If it stays wet you are likely to have problems with smell and health. I don't know how steep your areas really are so this is probably not an issue. But erosion might be. When you build on a hillside you can change water run-off patterns. It makes it a little more challenging.
My second criteria is your convenience. You are going to be going out there regularly to gather eggs. You will be carrying feed and water out there, winter and summer. Will you need to wade across wet spots in some weather? How steep is that hill? Where is your compost pile? Will you be dumping poop and bedding in it? I carry a lot of stuff from my garden to the chickens, how convenient is that for you? You are an important part of the equation. The more comfortable you are the better care you will take of them.
Heat is more dangerous than cold where you are but you can deal with that in either location. It requires clean water, good coop ventilation, and shade.
There are more issues to free ranging than just predators. Some people go years free ranging without any serious predator issues. Others get wiped out immediately. Any time you free range they are vulnerable. Some predators may take one at a time, some may do a mass kill. Don't try it unless you are willing to take that risk.
If they free range they can spend a lot of time where you don't want them to. They poop wherever they go. They might hang out on a deck or porch, maybe inside some outbuilding if it is shady so they poop on your lawn mower or other stuff. They may leave land mines for you or the kids to step in. They may like hanging out in the road, a traffic hazard. They love to eat garden stuff or scratch mulch, either in a landscaping area or the garden. some people are OK with this, it's not a problem. Or they fence them out of places like a garden where they don't want them.
You might consider electric netting or electric fencing to keep them contained and safe from ground base predators. If they are installed properly they work really well but they come with their own issues. You have to keep the grass and weeds from growing up in them, this can short them out. Especially in a hillside dead leaves, cut grass, or such can wash up against it and short it out. They do take maintenance but they can be very effective.
Good luck!
