I have bantams and several neighbouring cats that trespass all the time. Some of them are killers. But not chicken killers. Some cats lure and the chickens get a bit alarmed by them. But not the way they react on seeing a dog. If they see a dog they panic. One chicken once was ‘attacked’ by a playful young dog, but rescued in time.
In the 8 years I have chickens I lost a few to predators. One by a buzzard (probably), one by a fox (certain). And a few chicks to a rat that chewed itself through the netting (certain).
The cats never really attacked my adult tiny chickens. Are you sure it was you’re neighbours cat that killed the adult chicken?
That questioned, I wouldn’t trust a cat with chicks. Chicks are a treat for cats and many more animals.
Imo chicks need to be locked in against all kind of predators. Cats, quit a number of birds of prey , rats, … I only let chicks free range under supervision where the broody and I am in control.
Btw. Here we have no law that says that cats are not allowed to trespass. And I don’t mind they do. Because I don’t have rodents because of them.
PS and I don’t want an argument with all my neighbours. They are the ones that look after our chickens when I’m on a vacation.