Turning in your two weeks notice can be terrifying__because no matter how well you think you know your supervisor, you can never be 100% sure of his or her reaction. Will he be furious and insist on walking you out the door immediately? Will she beg you to stay, enticing you with an enormous raise? Or will he be completely civil and wish you the best of luck?
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.