You want your intent to be as direct as possible. You are leaving, plain and simple. There's no need to mention where you're going. You can discuss that with your boss (though you're not obligated to do so) and your colleagues if you want, but there's little purpose for including that in your resignation letter. That's especially true if you're moving over to a competitor__you don't want to create ill will in this letter or cause any drama.
Your End Game. When you hand in your resignation, it can kick off a bit of chaos__your position will need to be filled, but your duties will also need to be covered until they can replace you. As part of your resignation letter, it's a good idea to convey what your availability is during that transitional period.