There is a feral cat we affectionately named Mambo. She is very old maybe 15 years or more and was here before we moved here. She's good around the grown chickens but the chicks I keep put up in a small dog kennel (exchanged chain link with hardware cloth) with a house until they get at least her size.
Sometimes she does steal a few pellets from the chickens. She does kill a lot of mice and attacks snakes, dogs, foxes anything that enters our property. After 5 years she tolerates a little bit of petting
. I was surprised one day to see a huge dog sniffing around the pens and she literally started screeching and jumped on it's back with claws locked in..looked like she was riding him hehe but he never came back.
As far as your neighbor's cat, if you can't find a way to work around the cat to get the benefit of it's predatory nature, I would say capture it and take to your local animal shelter. Many of the shelters will loan you a trap for this.
Sometimes she does steal a few pellets from the chickens. She does kill a lot of mice and attacks snakes, dogs, foxes anything that enters our property. After 5 years she tolerates a little bit of petting

As far as your neighbor's cat, if you can't find a way to work around the cat to get the benefit of it's predatory nature, I would say capture it and take to your local animal shelter. Many of the shelters will loan you a trap for this.