There are a couple of issues here.
First of all, your neighbor (and pit bull owner) is obviously a bit irresponsible. Bad pit bull owners give the breed a bad name. But at the same time, there are alot of vicious dogs of other breeds, or unknown breed, that cause way more problems. The very name "pit bull" conjures bad feelings. When in reality, it is one of those cases of if you throw enough crap at it....
On the other hand, having shitty neighbors with a dog they can't control is a real bummer.
One thing you have to understand about pits, they are usually very people friendly, but HATE other dogs. Or other animals for that matter.
The problem here is with the owner.
I am a pit bull owner myself, and am resposible about it. I do it because I love my dog.
But at the same time, if this is a dog that isn't attacking people, I'm not sure that putting it down is the way to go.
Dogs will be dogs. I've had a big lab attack one of my pits before, and I don't think anybody would have called for putting it down.
I've seen alot of neighborhood dogs who were bullies, and almost none of them were pits. Yet they lived long and happy lives.