I've only done two, and they were very different kinds of trips. But they were both fabulous.
Best things: Being on a boat. I love boats. I love sleeping on boats. Sleeping on the top deck of the MV Tala, beneath a sky thick with more stars than I had ever seen in my life before, was an amazing experience.
Spending a period of time with other people who understand diving addiction.
No sand, no surf, no tides or currents to worry about (let the captain do that). Exits, on the other hand, can be interesting, depending on the techniques used.
No gear cleaning until the trip's over.
Bad things about liveaboards: EVERYTHING ends up damp. Boats are full of things that eat toes. The only exercise you get is whatever swimming you do when you dive. If you do the night dive, everybody who didn't eats all the dessert before you get back.
Whatever you break or lose, you're out of luck, unless the boat has one. (Unless you're on a boat like our liveaboard in June, with 23 standardized divers, many of whom had brought spares; we even came up with a spare DRY SUIT for somebody who ripped his neck seal!)
Overall, both of mine were fantastic experiences, and I'd be eager to do another one.