Also GREATLY depends on the dog owner and if they know to train a dog.......I really think it's more the individual dog, and what he sees as his responsibility, more than what breed it is......
To the OP: Get some fence!...it can take up to 2 years to properly train a dog to do what you want it to do....and they often need fencing anyway.
It sounds like you are renting? Maybe some electric poultry netting would work well in your situation, it's pretty easy to move to rotate ranging, it will keep most predators away and you can take it with you when you move.