We generally go on Celebrity, and the ships hold roughly 2700 people or fewer. They don't have rock climbing walls, ice skating rinks, water slides and all the amusement park stuff the really huge ships have. We tried one of the huge ships for a change this past spring, and decided "one and done"; we won't do it again. Too many unruly kids, too much noise, and too many lines.
As for the configuration of the ships, they are suitable for what they are used for. The only time one has tipped over was negligence on the part of the captain.