Well, you need to fall asleep to dream in the first place but other than that it's actually better to not be tired as you're most likely to end up in REM, that is if you haven't slept well or if you're going to bed for the night.

Dreams are not fuzzy because you're sleepy, there's a bunch of factors like if you're in REM, chemicals in your brain, amount of sleep you've gotten and your ability to recall dreams.