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 Date. The most crucial detail in a resignation letter is your end date. Legally and according to your company's policy, you might be required to give a minimum amount of notice (two weeks, or possibly more, depending on the company and the role). If that's the case, you don't want there to be any confusion about how much notice you give. If it's right there in writing in a letter dated two weeks before your last day, you're saving yourself the hassle.