This topic was necro'd by a spambot, but I'll summarize just in case.
There's currently two types of bed. Thatched Bed, and Sturdy Bed. Don't know of exact values but I'd like to assume that Sturdy Bed of any quality is better than any Thatched Bed.
Sleeping (logging out) in a bed will restore Travel Weariness (TW) that is when you fast travel. Current forms of fast travel are Hearthing (flat 0.1 points) Traveling to home dock with a ship (allowed even when exceeding your TW cap, puts you into 100% if you do), Traveling to a Charter Stone, and Traveling along a road (Wooden Signpost and Milestone.)
You will also regain SHP regardless if your energy is above the "healing" threshold of 8000. HHP wounds supposedly also tick down faster (this can be a problem if you have "Adder Bite" -wound, try to treat all your other wounds before sleeping to not get killed when the Adder Bite peaks.)
http://ringofbrodgar.com/wiki/Hitpoints