Was it not an option to just call and ask your neighbor directly to dial-it down a notch (or two or three)?
We have a neighbor right behind our house with a pool & teenagers. Occasionally their parties can run late. But we have a great relationship with them, where if we call over and ask them to turn their music down, they immediately do and apologize profusely. It's never occurred to us to contact police.
Because we've developed such a good relationship with them, our neighbors usually tell us ahead of time when they're going to have a larger party, and tell us in advance to let them know if it gets too loud, knowing that we have small kids who go to bed early. Some of the time they invite us!

And we do go to their parties sometimes... the kids love their pool.
Anyway, my point is just wondering if you might try to get to know your neighbors and then when you do, you could talk about the noise in a friendly way and try to work through it in a civil way where you both can get what you want.