The founders of the American constitution were challenged with an immensely bold undertaking: to address the problems faced by the colonies but do so in such a way that their solutions would pave the path for "a more perfect union" for centuries to come. Therefore they had to build a rigid but flexible structure, able to handle both the crises of the day and those of the future. In many ways they created a framework that has done just that—in other ways, at best, there were obstacles no one could have foreseen.
The largest of the discrepancies have stemmed from three main things: technology, political norms, and geography. Technology may be the largest unforeseeable factor: today our communication, governance, social glue, journalism, news reporting, and, therefore, democracy are all fundamentally changed by technology. New questions about the second amendment and gun rights are raised by entirely new forms of weapons in civilian hands. The internet has brought us self-publishing, which has shaken trust in established central news outlets, and instantaneous transmission, whereas communication in late-18th century America was done via horseback or stagecoach. Drones, missiles, and AI are changing our warfare and national security. The existence of smart phones and big data affect our privacy and central intelligence. When drafting both the protections of individuals under the Bill of Rights and the powers of the three branches of government, we have seen how simple wording in the Constitution can have profound consequences. Take, by example, how the wording "right to assemble" can be interpreted in an online context or how "a well regulated Militia" can be understood in the context of assault weapons, bombs, and gases designed to kill crowds. Granted, the Bill of Rights followed the founding of America in 1791, but the examples still stand as disparities in problems faced across time.
The second difference, political norms, is one that has changed in part because of the US constitution. The founders were responding to the central power of a king, whereas today we have presidents, prime ministers, and congresses whose powers are more distributed than monarchs of old. The difference, more broadly, is due to a general shift in regional powers from colonialism to tighter nation states and the constraining realities of nuclear power, economic warfare, cyber warfare, and global alliances such as the UN, EU, and NATO that shape global hegemonies.
The third major difference is a simple matter of geography. Some argue it was easier for Americans to fight for independence as colonial entities in America because they were separated from their oppressors by an ocean and had at their disposal a wealth of resources and land (after they had committed terrible genocide against the many indigenous populations existing before them). Any separatists and secessionists of today's America will find it much harder, as the South discovered in the mid-19th century.
I chose to end with the similarities between the problems the founders faced and those that exist now because I find them far more compelling. Of the similarities of great significance are the troubles imposed by a tyranny of the majority, the danger of factions to democracy, the power of money to corrupt, the threats misinformation and alienation of news sources bring to the people's right to free press and sharing of information, the damage to national security caused by degradation of trust in intelligence agencies, and the conflicts of interest held by a governing entity having lasting consequences. Many of the beliefs held by the founding fathers were to thwart these various threats against democracy and to create institutions that could withstand them. By drafting checks and balances between the executive, judicial, and legislative branches of government and by preserving freedom of speech and the press as a fourth check on the government, the founders hoped that the nation would continue to build on its good assets while fortifying against the corruption that has so often toppled former regimes. They also hoped to eventually purge the country's inherited habits of oppression, as was the case with institutionalized slavery (a slow process). The current dilemmas we face today that we share with the colonies are more important than ever.