How are debates over American foreign policy in the years since 9/11 similar or different to debates over American foreign policy during the Cold War?

When the Berlin Wall was torn down in 1989 and, two years later, the Union of Soviet Socialist Republics disintegrated, the debate over the future foreign policy challenges and opportunities in a post-Cold War world focused primarily on what was called “asymmetrical threats” to U.S. national security. Policymakers debated the steps that should be taken with respect to the former Soviet republics suddenly, and unexpectedly, independent (e.g., Ukraine, Uzbekistan, Estonia, etc.). “Asymmetrical threats” refers to the potential growth in military and political problems associated with non-state actors, such as terrorist organizations, organized crime, unaffiliated cybercriminals, and so on. Absent the compelling threat from a major military power like the former Soviet Union, it was considered unlikely that another major power would soon emerge to rival the threat once posed by the Russian Empire. U.S. foreign policy, consequently, lost its focus to a large degree, the Cold War having provided a certain eaily-defined structure and predictability now lacking. China was not yet the focus of attention except in the contexts of international trade and the situation involving Taiwan, which the Chinese view as a breakaway province and the native Taiwanese as an independent nation-state.
If US foreign policy lacked focus, that changed dramatically with the terrorist attacks of September 11, 2001. Prior to that date, al Qaeda (Arabic for "The Base") was the principle target of US counter-terrorism policy, but was not yet receiving the level of attention some terrorism experts in the US government believed was warranted. Immediately after the 9/11 attacks, however, al Qaeda and terrorism in general became the primary focus of foreign policy. The administration of President George W. Bush viewed the attacks by al Qaeda and its leader, Osama bin Laden, in the gravest terms. In his first speech before Congress on September 20, President Bush notified the world that the war against terrorism was being considered an existential threat, and that the stakes could not be higher:

This is not, however, just America's fight.  And what is at stake is not just America's freedom.  This is the world's fight.  This is civilization's fight.  This is the fight of all who believe in progress and pluralism, tolerance and freedom.

By presenting to the American public and the world the threat from terrorists as existential, the president was also notifying the world that the era of studied neutrality on the part of so-called non-aligned nations was effectively over. In one of the president’s more consequential statements, which occurred in that same address to Congress, President Bush declared to the world, “Either you are with us, or you are with the terrorists.” This statement had major ramifications for U.S. foreign policy, as many nations around the world did not believe they had a particular need to choose sides between the United States and its allies on one hand, and Islamist militants on the other hand. Bush’s comment, then, was seen as unnecessarily polarizing, despite the fact that state support for terrorism had been a serious problem since the 1960s, and remains so today (see: Iran).
While the struggle against Islamist terrorism became the primary focus of foreign policy, the Bush Administration was also focused heavily on Iraq, which some within the Administration viewed as complicit in the 9/11 attacks, despite the absence of compelling evidence to support that assertion. While Iraq was heavily involved in supporting terrorists, its focus was mainly on terrorist organizations that targeted Israel, which Iraqi dictator Saddam Hussein hoped to destroy through the development of nuclear, chemical and biological weaponry. Allegedly unbeknownst to the U.S. Government, however, was the fact that Saddam had decided to get rid of his banned weapons programs in 1998. On the premise that Saddam still had these weapons, and that his regime was tied to al Qaeda, the president decided to launch an invasion with the intention of removing Saddam’s regime from power and replacing it with a democratic form of government. The subsequent invasion and its still-ongoing aftermath fundamentally changed the Middle East and, with it, forced more attention on that region than the American foreign policy establishment had anticipated.
U.S. foreign policy today is confronted with myriad challenges, from a resurgent Russia to a rising China to intractable conflicts in Afghanistan, Iraq and Syria and the relatively recent problem of the rise of the Islamic State. In short, there is a plethora of foreign policy challenges confronting the United States and no real answer to any of these assorted problems. The Cold War, as serious as it was in terms of the nuclear stand-off between the two superpowers, was, at least, easily definable in terms of the scale and nature of threat to U.S. interests. The post-Cold War world has lacked that level of clarity and forced the foreign policy component of the federal government to think in entirely new terms. The “asymmetrical threat” posited after the fall of the Berlin Wall certainly materialized, but in far greater intensity than anticipated. And, the rise of China as a military and economic force with which to contend in the Asia-Pacific region, combined with Russian President Vladimir Putin’s determination to reassert his country’s role on the world stage, have resulted in a more complicated and potentially dangerous world. U.S. foreign policy no longer has the luxury of focusing on a single major threat; the threats today are more varied and less predictable.
 
https://georgewbush-whitehouse.archives.gov/news/releases/2001/09/20010920-8.html