So pretty much I should stick with Hardware Cloth? What size and gauge?
Edited to add: Use 1/2 x 1/2 or 1/4 x 1/4. Smaller holes = harder for predators.
If you use the welded wire just be prepared that one day you will take a loss from it.
Like I said I use it.. On everything. Cages, pens, etc. I know losses will come but its pretty tough stuff over all.
Hardware cloth beats it a hundred times over, when used correctly. Its also a pain to cut and can be difficult to work with. Not so much like that welded wire you have pictured. Its all up to you, in the end, as hardware cloth can be expensive. I don't use it on anything except the quail and rabbits for that reason only. If I could afford it on all of my pens, I would use it.
Raccoons, opossums, skunks, they can all reach through the welded wire. If they can grab your birds, they'll pull them through one piece at a time. Bigger predators will just rip the wire.
Hardware cloth is stronger and has smaller holes, making it much more difficult for predators. If applied correctly ( I.e. Bolted down not just stapled )