There are no absolute measures for what defines the best moving company available. There can be different criteria that hold more weight then others with certain people, but overall, I would say that the best moving company is one that handles valuables safely while still offering a fair price. There are other factors that could help define what the best moving company is, and to some, they may influence the decision to pick one company over another.
Punctuality should not be underrated. There are critical windows at times with moves, and the best moving company should be one that shows up at the scheduled time and is ready to make the move. They should also not lag or purposely take their time during the move process, besides being painstaking with items that demand extra time and attention during the move. There is also something to be said for the customer service skills of the movers themselves. Some clients can be a bit demanding, but the best moving company should have movers who remain polite and level headed during the move.
Of course, back to the core elements. To truly be called the best moving company, they need to take the greatest amount of care in moving personal belongings and furniture. They should also insure their move properly to pay for any damage, which at times can be unavoidable. This should also be done at a price that is not astronomical, although a concerned client may pay a few dollars more if the mover has a solid reputation for being the best moving company in the moving business. Once that reputation has been well established, it will promote the moving company through word of mouth and generate business based on customers relaying their positive experience to others. Being known as the best moving company in the business is excellent marketing.