Ummm, I had a real problem with the neighbors big tom cat about a month ago. I witnessed him several times stalking my free range bantams, and he came too close to catching one a few times, so I called the neighbor and told her what would happen if she didn't keep him off my property. Well, he caught a hen one morning and tried to tote it off under the feed shed but I stopped him. He didn't kill it, but he would have if I hadn't been around to stop him. I called the Sheriff and he told me to talk to the neighbor and I told him I had and she said she couldn't do anything so he told me I had the right to protect my property if he tried to attack again. Next morning, hubby was home and again, the cat attempted another attack right in front of him so he took him out. We both hated for it to come to that, but sometimes you just have to do it.
I did call the neighbor to tell her what had happened, and while she wasn't happy about it, she really had no choice in the matter, especially after our previous warnings.
We have dogs and cats too, but we don't let them run loose causing problems for others.