Depending on your assessment of predatory risks for your location and your planned routine (ie chicken door open 24/7 or chicken door closed with birds inside coop dusk to dawn, etc) you could hybridize the two by using the welded wire as a "skeleton" to avail yourself of the increased strength with poultry netting over the top to keep smaller birds and chicks from being able to get out of the 2x4 openings (you'd be surprised at the spaces these guys can squeeze through). Poultry netting does little to protect birds or keep any sort of predator out. If you want to increase the security add a couple wires of hot wire powered by a good, strong charger. Add a nice "no dig skirt" around the perimeter (use the welded wire for this, not poultry netting) and you'll be in fairly good shape.
My run is a hoop coop style run constructed of cattle panels and covered in poultry netting - with hot wire. My assessment of the risk for our particular location is that the primary threat is nighttime (that is not to say that daytime risks don't exist), so I have the birds cooped from dusk to dawn because the coop is more predatory resistant than is the run.