Seems like us hammock folk sleep better, at least in places where we can hang. Comfort aside, being above the ground, especially in wooded areas with lots of critter action going on, I feel like I am above the fray. I've hung in a swamp and watched poisonous snakes under me with no bug net and never stressed...and I ain't no Bear Grylls. That would have freaked me out on the ground, but then again, that would never have happened in a decent campsite in the mountains. The perspective raises my comfort level and confidence I suppose. I live in the southeastern US and find that I only truly sleep like a baby on the ground in the winter and when I'm out west at or above treeline. If I'm deep in the woods or some other thick vegetation area, I guess I treat a hammock like a tent--it gets me out of the line of fire, at least mentally--and then I feel the wind, the sway of the trees, I can see and hear better, and I zonk out easily and stay asleep. Peeing out of a hammock is easy too...
I think we all go through some fear of the unknown, and that surely affects our sleep. Don't remember where, but I remember reading a hysterical story by a guy who stayed up all night after something hit his tent and he kicked it off. Turns out is was a hiking pole, but he imagined all kinds of things. If anyone knows what I'm referring to, shoot me a link. I'd love to read it again.
Don't take sleep meds, even something like Tylenol PM. Even if it means you lose some sleep, you'll gain a lot more from the experience without them and you won't wake up groggy.