Sorry to hear about your delimma.
What you've got on your hands now is an immature grown man with a bit of a control issue and a lack of golden rule knowledge. This guy lives next to you, and in his head this is the biggest competition of his life and he Must beat you in order to feel secure in the end of this whole thing.
If it were me, at this point in time, I would be thinking through what's going on in his head...ask yourself "why is he like this?" You need to realize that this is the same kind of irrational immaturity and insecurity that leads to many violent crimes. Option 1, show up at his door...tell him you are sorry that you offended him last night. Tell him that you were upset at the time because you wanted your sleep. These things are all true, unless you actually did mean to offend him, in which case you should stop reading this and go ahead and start the imminent redneck fistfight in your driveway. By doing this, you're telling allowing him to make the decision that you're not such a bad guy and he has no quarrel with you and in his mind you aren't someone he has to prove wrong. If you can say something like "You were absolutely right about it being a free country." Same method that you use when you've got to dump an insecure girl, lead her to the decision to cut it off so you don't have to worry about getting phone calls for a month or her showing up at your door or questioning 'what's wrong with me?'
option 2, as I stated before, is to maintain your pride and "win" this argument. Call the police, pray, whatever you need to do to win...go to a higher power. I guarantee this option will invoke some anger in your neighbor, and you will butt heads until one of you moves. It's just a big game, just like road rage.
Or you could just take my advice with a grain of salt, but I'm about the closest thing you'll find to your jerkwad neighbor who holds a double standard to the golden rule. I've been in the same situation before, except they did call the police and I turned my stereo down, then I took the low road until they eventually moved, then I felt kinda lousy at first, but now I just tell myself that it was just a game and they moved because they wanted to. It's not like they told me it was my fault htey moved or anything.