My personal (stress personal) preference, is for closed in on top. Either way is fine - a big fenced area or a big run, it's all the same to the chickens as long as they have space to prevent overcrowding. Closing it up on top can reduce the risk from overhead predators and gives you a firm base if you want or need to tarp it for any reason. Trying to tarp or cover a fenced in area without a top on it guarantees that the tarp will sag in the middle and it's hard to get it tight enough. Now that said, even a covered run or fenced in area can have a sagging tarp on top - it depends on the weight of the accumulated snow, rain, or leaves on top. But at least a cover gives it something to sag against. The other thing to consider is small birds. Believe it or not even family of sparrows could - and I repeat, could, not absolutely will - bring in stuff that you likely don't want in your chickens. There is probably no such thing as a totally mite free environment for the chickens, but letting small birds in is a pretty sure way to introduce the little pests. For those reasons I chose to cover my run. But your situation might be entirely different than mine, so I think in the end you'll look things over carefully and make the decision that's right for your setup.