I have a friend who's a trumpet player who has it. He can lay in bed and write out an arrangement, whereas most of us mere mortals would need to reference a piano or a guitar.

Other than that, it's mostly a cool parlor trick. The best story I've heard of someone who had it is that of Woody Shaw, the great jazz trumpet player. A piano player tried to test him on it once, and played a bunch of different chord voicings -- Woody correctly identified all the notes in each of them. Then, to up the challenge, the piano player played a random cluster of notes. Woody listed them all out, and the piano player replied, "Wrong," thinking he had finally stumped him. Then Woody replied, "Now take every note I just said down by a half step." Of course, Woody got them all right, and everybody's mind was blown.

> He can lay in bed and write out an arrangement, whereas most of us mere mortals would need to reference a piano or a guitar.

Why wouldn't that be the case with someone who can "only" hear relative pitch? I mean, you start writing a note and from then on all other notes are relative to that note, where the actual pitch (in Hz) doesn't really matter.

Right. It's perhaps useful if you're a musician (though I'd argue having relative pitch is much more useful), but otherwise it just feels like an annoyance that will reduce your enjoyment of many everyday musical things.