Cats: Inside or Outside?

Do you ever let your cat(s) roam outside, and simply call them in for meals or to sleep at night? I don't. This isn't a matter of pride for me, but rather a matter of loving my cat and respecting the property of others. My cat, Pippa, stays inside at all times, unless I specifically let her into our backyard and keep an eye on her. Cats don't need to be outside at all times, and shouldn't be left to wander freely.
We have recently encountered some problems with the cat(s) of our neighbors. They let it out during the day and don't even call it in at night, which means that it could actually be a stray cat as our neighbors say it is. It (or a different cat) has already peed on our porch decor, and has ruined the cushions of our outdoor furniture.
When we informed our neighbors of these incidents several times, they suggested silly things like spraying the cat with water when we see it or putting towels on our outdoor furniture so it can have a place to sleep at night. The fact is, these ideas are ridiculous. We are not going to take the time to spray someone else's cat with water at 3:00 am, when it is harassing my cat through the window. We aren't going to put towels on our furniture, because it shouldn't be on our furniture in the first place.
I love animals and I wouldn't harm the "stray" cat, but I also wouldn't purposely inconvenience myself so that another person can be irresponsible and lazy with their animal.
This whole thing confuses me, because I want to know why people think it is okay to leave their cats outside, but not their dogs. Why are cats so different from dogs and other animals? Don't fool yourself into thinking that you're doing your cat a favor by letting it play outside anywhere it wants. Have you noticed how many cats get killed by cars and other animals? Wandering cats are also a big inconvenience for people who slam on their brakes just to miss a cat that's running across the road, or people who have their outdoor furniture destroyed.
The one time that my cat got out (we had our door open for air because my mom was painting inside), we immediately looked everywhere for her. We finally found her near our front door, and were relieved.