1. Probably no unsolicited mail through the US post office is being opened in Congress these days.
2. The express mail has your correct name and address clearly identifying you as a voter in that person's district/state.
3. Someone in the office has to sign for the delivery of the letter.
4. It has the look of an important piece of correspondence and thus immediately attracts more attention (good attention, not scary attention).
5. It shows that you are serious enough about this issue to invest a few dollars in making sure that your opinion is heard.
Also, I completely agree with the advice to be polite but firm. We are writing these letters for maximum result, not to blow off steam. Blow off steam here in the forum, write letters to your representatives with results in mind. Best to include some statement about, "your action on this issue will determine whether or not I vote for you in the next election".