I have heard the mail method called "common law copyright." While it could probably be used as evidence in court it is certainly not as strong a claim as registering with the government. In the US the any publication or recording is automatically protected by copyright and you should inidicate that on the document along with the date. In any dispute, the prior publication (I guess this would include mail) has the stronger claim. Government registration is the strongest evidence.

One thing to remember is that the government does not do any research on whether you are the author or not. They take the money, datestamp the form and file it. That records the date you offically asserted your claim of authorship. If someone else registered the same song the govenment would happily take his money and stamp his form too.

It is worth the money to register but if there is a dispute you could still end up in court. On the plus side, songs are seldom challenged unless they make a lot of money.