“Inform your neighbor that their dog is asserting aggressive territorial behaviour well beyond their property line, and that that could lead to huge liability problems if the dog actually attacks someone. “
I took that tact and my wife almost paid the price. Dangerous dogs need to be addressed now, not after they kill someone.
But if you don't point out to the neighbor they are being idiots about the dog, they might never know (some can't figure it out on their own). This isn't some renter, it's the new owner.
If you can't get along with the dog, and can't get along with the neighbor, call the police. If they won't do anything, be ready to take whatever defensive measures you deem prudent.
Your actions might make a new friend or might start a lifelong feud with the new owner--it is up to you.