There's a story, almost certainly apocryphal, of some famous writer having a dream where he wrote a poem, and everyone lauded it for its subtle insight and wisdom. He woke from the dream, and quickly, before the dream faded, grabbed pencil and paper and wrote it down. Then, satisfied that he'd preserved that gem, he went back to sleep.
Next morning he looked at it, and found this:Hogamus, Higamus,
Men are polygamous.
Actually, I can give you a non-apocryphal version of that story. For many years I composed music as a hobby. Like anything else, eventually that gets into your dreams. Many times in my dreams I composed masterworks that would forcibly move you to tears by their sheer awesomeness, but I could never remember them.
One night I finally managed to drag the melody line of one of them up to the waking world. It's not even worth taking the time to find a program to do musical notation with. My masterwork of surpassing genius, in two-second-long quarter notes: C, C, D, C, and repeat.
While that melody line certainly could potentially lead to tears in the eyes of listeners, I doubt it would be due to sheer awesomeness.
There are a few anecdotes about people solving problems in their sleep, but I'm inclined to think that is actually far, far more rare than people dreaming they have solved the problem in their sleep. Sleeping on a problem is well-documented to improve performance the next day, but I think that's more a result of whatever general maintenance and idea shuffling is going on than the direct creation of good, concrete ideas at night. I think it makes it easier to come up with good concrete ideas upon thinking about it while awake.
In fact, come to think of it, this leads me to what would be my first explanation of why night owls are more creative. I've noticed that some of my most creative writing occurs when it's not just late, but I'm actively sleepy; I'm assuming that some of the inhibition and judging parts of your brain are getting shut down. Consequently, in many ways, as you'd expect, it's also some of my worst writing; bad leaps of logic, horrible spelling and grammar, things that make perfect sense to me (even the next day) but are not explained well enough for a reader to understand, etc. Slipping some more stuff past the part of your brain that judges things before they even make it to conscious thought can lead to less inhibited and more creative thinking, although I wouldn't want to function that way all the time. Night owls may simply live an inch closer to that state all the time than morning folk, and this could easily affect sleep cycles in predictable ways, though I wouldn't care to guess the mechanisms.
Having this sort of the diversity in the species is good; both ways of functioning have advantages and disadvantages.
When you're dreaming, I think these judgment circuits are basically shut off, and as a result it's really easy to think you've got a brilliant idea, when in fact you've got anything from something physically possible but basically useless, or potentially even no actual idea at all, just a general sense of awesomeness. Every once in a while by sheer luck you may connect a snake eating its own tail to benzene, but only after filtering through who knows how many thousands or millions of less useful ideas.