It depends on the size of your dresser. If it’s a small and light dresser, then you can keep your clothes inside. If it’s a big and heavy dresser, then you should take them out. The main reason movers like having dresser drawers empty is to reduce the overall weight. You should also tape the dresser drawers shut so they don’t fall out. If you don’t, the movers may simply take out the drawers, but that would take up more space in the moving truck.