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.
State Your Intent. The whole theme of your resignation letter is the statement that, well, you resign. You don't need to play coy__the time has passed for you to fish around for a counteroffer if it's gotten this far. At this point, you've made your decision to leave, and this letter needs to reflect that.