Most of the time the threat posed by LGDs to predators is enough. Most predators know that if they are injured they could die. When the predator refuses to leave you want to have LGDs to go after them. I prefer my LGDs to chase off the predators without tangling with them and getting injured. 1 or 2 LGDs couldn't take down a cougar or bear but my hope is that they scare it off before it take any of my livestock. A friend who breeds Anatolians in TX had 2 14 month old and 3 10 month old Anatolians in one enclosure when a large cougar came in. The cougar had been taking goats, sheep, and hogs for months in the area and decided to come in after the young dogs. The 5 puppies killed the cougar but it was a bad fight and several were badly injured. They all recovered though it took some time for one of them.
Dage: If you have mostly dog or coyote predators, a llama might be a good choice. Donkeys are also good choices. If you have cougar, or any of the big cats, bears, or wolves, then LGDs are the only choice. Although I have seen pix of a mule attacking a cougar and killing it. Where exactly do you live?