If You Want to Do More Than Just the Basics with Your Resignation Letter. You can always write more, and craft a longer resignation letter, but the truth is that it isn't necessary. You can add a portion of the note where you thank your manager or boss for the opportunities and time you have had together, or add that you hope to keep in touch, but in reality, if you really feel this way you probably should make an effort and find an opportunity to say these things in person (rather than getting an email).
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.