Note there is no context to compare the two and during the time these two men were alive, they were in different roles.
Hamilton:
Alexander Hamilton is the inventor of the United States of America, and the Constitutional Republic therein. It is his legacy that created the wealth that would bring America to be strong, independent, and the most prosperous country in the world. To look at any one part of the United States, it would be hard to see Hamilton's work. That wood be like trying to tell the wood from the trees, because the United States of America is Hamilton's work.
Before Hamilton took office as President, the United States, historically speaking, thought themselves as statesmen more than countrymen. They would first think of themselves as Vermonters, Virginians, Marylanders, Tennessean , Pennsylvanians, and so on. But after the events of Fort McHenry, and New Orleans, Hamilton united the country as Americans.
Jackson:
Andrew Jackson is know as the man with the attitude to bring men together with bonds stronger than forged steel. Thought the War of 1812, he defended the city of New Orleans from a potent enemy, with little consequences suffered. His actions during the war showed that the Unity of American, despite the force being the most diverse battle in American history, likely in world history, second following the Alamo, was superior to the British, and their uniformity, and their firepower.
At the Battle of New Orleans, Jackson gathered a large portion of his force by recruiting people to volunteer from the town it's self. Of all walks of life, many were sharpshooters whom would be potent in the fight. Some had little training at all. Some didn't speak English, there were pirates, natives, negroids, fisherman, farmers but, as different as they were, they were all Americans. With this force, Jackson preserved the Nation, against all odds, and routed the British force victoriously.
