I don't think cats even have the same status here. In this country we have a "summer cat" problem. I don't know if you have the same phenomenon in your respective countries, but here some people get a kitten just for the summer and then just discard them when fall comes, either because they haven't thought about how to take care of the animal once they move back to the city, or because they just don't care. Naturally, the cats won't survive the winter, so these animals fill the shelters every year. But I think there has been a huge improvement, cats are routinely sterilized these days. I'd say it's definitely a rule rather than an exception. In fact, I don't remember when I last saw an ad for somebody donating or even selling kittens. I'm probably just not paying attention.

When I've been on vacation in southern Europe (especially Greece, but also Italy, Spain, Portugal and Cyprus), there have always been a lot of cats everywhere. I have no idea if they have owners of any kind or if they're "public property", but they seem very much a part of the scenery. I'd love to know if they're considered much of a problem.