If Hamilton and Jefferson could see our nation now, which of the two would feel like their ideal was realized, or neither?
Hamilton would feel that his ideal was realized more than Jefferson would. Hamilton dreamed of an industrialized nation with a strong domestic industry, while Jefferson dreamed of an agrarian society with a prominent role for the self-supporting farmer. Although industrialization began before the Civil War, following the Civil War the United States underwent a period of rapid industrialization and became an economic and industrial powerhouse by the turn of the 20th century. This is a role it has maintained (while turning to outsourcing for some of its production) to this day. Therefore, Jefferson's idea of agrarianism, which the South clung to well into the 20 century, was largely outdated even by the Civil War, as the nation as a whole turned to manufacturing.
In addition, Hamilton supported a strong central government and the Bank of the United States, while Jefferson believed the states should have more rights and powers. This was one of the central debates, exemplified through slavery, that provoked the Civil War. In the end, the federal government became stronger during the Civil War and in the 20th and 21st centuries with entitlement programs and agencies such as Social Security, Medicare, Medicaid, and the Affordable Care Act. The states have lost power in relation to the federal government, and it is explicitly stated in the 14th Amendment—passed after the Civil War—that the states cannot abrogate the rights of individuals. In addition, the United States has the Federal Reserve to oversee the nation's banking activity. Hamilton's vision of a stronger federal government became reality, while Jefferson's vision of a country with strong state governments was less predictive of the future of America.
Hamilton would feel as though his vision for America had been fulfilled. America is an industrial and commercial giant with trade networks all over the world. It has close ties with Britain and it spends more on its military than the rest of the world combined. The Federal Reserve provides banking stability to banks all over the country by regulating interest rates and monetary supply. Hamilton also would favor the strong federal government over the state governments, though I think he would have many questions on entitlement programs which involved people on a very personal level. He would enjoy the interstate system, however, as this was the ultimate internal improvement.
That said, Jefferson would find parts of America that he liked as well. While he would not be a fan of federal oversight, he would be happy that the slaves were finally freed. He would also like the national park service and that millions of Americans were still engaged in agriculture. He would be happy about the level of freedom of speech and how the nation sought to challenge inequality.
Neither Hamilton nor Jefferson would approve of the regressive tax system. Jefferson would not like it because of federal overreach, and Hamilton would not like it because it would hurt the industrialists more than it hurt the laborers, which means he would find it unfair.
For the most part, Hamilton would feel that his ideal had been realized in economic terms while Jefferson would be more likely to be pleased with the political system.
Hamilton wanted a nation in which manufacturing and business dominated the economy. Jefferson believed in a nation of small farmers who did not work for anyone else. We are clearly not a nation of small, independent farmers, so Hamilton's vision is closer to our present reality.
Jefferson wanted a society in which all people (slaves aside) were equal while Hamilton wanted more of a hierarchical society. Today's society is aggressively egalitarian. We do, of course, have inequalities of wealth, but we firmly believe in the idea that all people are equal. This would be more in line with Jefferson's ideals.