It wasn't because Lincoln was President of the North that resulted in the North winning. So yes, the results would have been the same. Both men were heavily involved in the affairs of the war. But Davis had more problems to deal with than Lincoln, problems that included feeding and supplying his troops, dealing with governors who tended to be more resistant to the government, an ever tightening blockade that was slowly strangling the Confederacy to death, and man power. Had their roles been reversed it would have been Lincoln who would have had these problems forced on him.