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I don't care about who's property is where. Shooting one's neighbors' pets is not a nice thing to do. I wouldn't want anyone who would do that as a neighbor. Unless the pet is posing a genuine physical threat of some sort, I would advise anyone to find some alternative (non-lethal, non-harmful) means of dealing with the situation.

Finally, dogs and cats are different. Dogs are emuch more easily controlled. In many cases, the law requires it. They are also (some breeds) much more likely or capable of posing a physical threat.

Cats are almost impossible to confine unless kept strictly indoors. Cats are also much less likely and/or capable of posing any sort of physical threat.

Shooting or (as I have heard that some people do) poisioning someone's pet is a very hostile thing to do, and frequently leads to trouble. Unless you want to read about yourself in the paper, I wouldn't advise doing it.