If you are replacing the chicken wire, you will want to opt for something smaller than the 2"x4" welded wire or you will be fighting off wild birds. Ask me how I know. Plus, anything can grab a chicken or duck through that size of gaps without added protection like a hot wire.
I have the 2"x4" because the guys installing told my husband if a predator is going to get in, they will get in no matter what. I remind him every day when I go out there and have to deal with wild bird crap.
I have an electric hot wire around the bottom at 3" and 6". I recommend 3" up due to snow. I sweep it off, but keeping up with snow on the bottom wire can be an issue. I do have an issue with a fox, but it has never gotten into the run. No digging and no jumping. The hotwire keeps it away. Plus, the run is like 8 foot tall and covered. I don't have any other predators that come into my yard, but I am surrounded by them as we live in the country. I also have an apron dug around the outer edge of the run.