It would be a great choice to hire one company to do both works, packing and moving. Through this, you can save cost, and if your item gets damaged, it is only that particular company's responsibility to bear the loss. On the other hand, if you hire different companies for packaging and moving, and if due to anything, your package will get damaged, both companies will blame each other, and the things will only get messed up, and you will not get anything.