If you live on a lifestyle block or something similar then nothing wrong with having a cat. IMO its just cruel to keep cats in suburbia, let alone locked up behind closed doors all day/night. The ones that do go out are certainly going to be a menace to your neighbors.
What about a bunny or two? Our kids have 2 bunnies. I built a nice large hutch for them so they stay outside. They are actually very good pets for kids. Many people in the UK even keep them inside and apparently have them house trained.
What size cats would you need to menace the neighbours?!
I don't think size really counts. Anything that eats meat and comes into my yard and poops is a menace. Its hard to be the good neighbor sometimes, best to just live with it and try not react. But I must admit it is sometimes very tempting to throw the stuff over the wall.