The short answer is it is best to empty the “large” pieces like dressers, chest of drawers, armoires, wardrobes, buffets, china cabinets, and desks.
The items that have to be moved have to be moved some way by someone. The question is what is the most efficient and cost-effective way. There are large bedroom pieces which physically cannot tolerate being moved full. “High-boys,” for example are in danger of having their legs snapped if moved full. Others can only be moved full with the assistance of special equipment like a refrigerator hand-truck. Often this is fine if it is a ranch house with old carpet floors. But in a multi-level house with hardwood floors—now you have to worry about damaging the floors.
Many Movers will say as a marketing ploy to “just leave everything full,” but when they need to, they will take the drawers out anyway.
For the drawers you do leave full, remember to go through them and check for valuables like currency, watches, jewelry, and firearms. You would be amazed how many people do not do this even after being reminded to. Many people have more loose valuable items like these than they can keep track of, and simply forget they are being kept in back of a drawer.
One time we were carrying a dresser down the stairs; a drawer opened up; a pistol fell out and to the ground and went off !!! Fortunately it was just a “starter pistol,” but we didn’t know that when we heard the gun fire.
Since the Movers may remove drawers and move them separately, think about the contents of the drawers and whether you want them being waved in the breeze. You probably won’t mind if the contents are pants and sweaters, but how about underwear and other bedroom items? Discrete, professional Movers will concentrate on their task at hand, and have seen everything anyway, but it is something to keep in mind.
In another situation, a long dresser may be not be all that heavy, but in order to get out of the bedroom it has to be stood up on end. When this happens, if the drawers are full–many loose items will be thrown against the side of the drawers (now pointing down), and the structure of the dresser will be tested. A quality dresser will hold together, but a press-board dresser may fall apart right then.
The conclusion: empty the drawers of the large pieces. The move will go faster if all the drawers are empty, but then that means extra work box-packing—whoever does it. A good compromise is to just leave “full” the “medium” and “small” pieces.