There are two things you might be talking about -- one is that very thin hard-to-see plastic netting, and the other is indeed called "plastic hardware cloth" on its label (or something like that anyhow) and is a much thicker stouter product, the versions I've seen have been grey, it is more like a miniature version of plastic snowfencing.
Either one will help keep chickens in and birds of prey out. The stout grey stuff will do a more-guaranteed job vs birds of prey, I expect (people occasionally have hawks get in through, or get tangled in, the nearly-invisible netting), but I am not sure it'd do ENOUGH better job to justify its considerably higher price and the fact that it will catch snow a lot worse. (Both will come down in any appreciable amount of snow, though).
Neither one will keep anything else out, though.
Pat