I think that is going to depend on what kind of predators you have. If you have something small like weasels, they can get through holes that big.
The wire on my chicken run is the size you are talking about. The only predator that I have had to worry about so far is dogs. If I begin to have a small predator problem, I will rethink my situation.
The wire keeps the chickens contained just fine, but four feet tall will not keep them from flying out. My run has wire on the top, too.
In a couple of months, I'm going to be moving some younger pullets into the run. Before I do that, I'm going to take the same 2"x4" weld wire and put another layer around the bottom for about two feet. But stagger it, so it makes smaller holes around the bottom.
I probably would not recommend that someone go out and buy 2"x4" weld wire to make a chicken run. Chicken wire and hardware cloth are the best. But I had almost $100 worth of this wire on hand and I wasn't about to go out and buy something more when this perfectly good stuff was right there.
So evaluate the size of your chickens and the size of your boogers and it will help you decide what to do.
Cassandra