I suppose it all depends. For example: my friend's next door neighbor had an invisible fence for her basset hound. One day, when the basset was outside, some stupid kid tried to steal the dog. The basset, of course, got shocked continuously and got hurt pretty badly. And hopefully, you can catch a dog before he digs under a fence or tries to climb over it. When my dogs are outside I check on them every five minutes to see how it's going. In my opinion, a real fence is safer. But it all depends I guess.

Well if I could get a real fence it wouldn't have to be anything special, my dog has never offers to jump the baby gats in our house that we use to keep her in certain areas of our house. Digging she only dose on exposed dirt and any time she dose that she gets scolded. The fenceing I was looking at isn't chain link, you can get it at any hard ware store in rolls but it's about $50 for 100' not conting the post you would have to buy to keep it up.
Still I don't know if I can talk my dad into letting me fence even a small area for her.