When you carbonate in a keg using priming sugar you'll still need a propellant, in this case CO2, for dispensing. Without a constant pressure applied the pressure in your keg will decrease, incrementally, with every bottle you fill. As pressure drops, CO2 will come out of solution and the carbonation level of each bottle will be slightly less than the previous one, until you're left with very little carbonation at some point, and likely not enough pressure to dispense the remaining beer. Assuming you don't have the ability to chill a keg of beer, you'll also likely have a problem with excessive foaming when filling bottles.
A set amount of priming sugar will produce a set amount of CO2 when metabolized by the yeast. When fully carbonated, your beer will have reached equilibrium, a point where the beer won't absorb any more CO2. A larger volume of head space will require more CO2 to reach a set pressure. Approximately 53, 12 oz. bottles (5 gallons) have more combined head space than a Corny keg filled with the same 5 gallons of beer, so will need more CO2 to achieve the same carbonation level. Because gasses compress much more readily than liquids, the amount of additional CO2 needed to achieve the same carbonation level in the bottles will be considerable more than the volumetric difference.
