Both men would detest the thought. But, in crucial respects, the foreign policies of Donald Trump and Barack Obama are looking strikingly similar.
The wildly different styles of the two presidents have disguised the underlying continuities between their approaches to the world. But look at substance, rather than style, and the similarities are impressive.
Both Mr Obama and Mr Trump have sought to disengage the US from the Middle East - a policy that has caused much tut-tutting in the Washington establishment, the group derisively labelled "the blob" in the Obama White House. As they pulled back from the Middle East, both presidents focused on Asia instead. Mr Obama strove to make a "pivot" to Asia the signature foreign-policy of his period in office. And Mr Trump has also made his two biggest foreign policy plays in Asia - through a trade war with China and nuclear talks with North Korea. Increasing suspicion of China and growing concern about the Korean nuclear programme were also themes of the late Obama years.
The two presidents have both had to appeal to an electorate that is profoundly war-weary. As a result, both Mr Obama and Mr Trump tried to cut back on America’s global military commitments in ways that have alarmed not just the blob, but America’s allies too.
That concern underpins the uneasy atmosphere as the Nato alliance gathers for a summit in the UK this week. Mr Trump's vocal discontent with Nato is often portrayed as a stark departure from the American norm. But it was actually Mr Obama's defence secretary, Robert Gates, who warned in 2011 that the future of the alliance would be "dismal" if Europeans continued to rely on the Americans for their security.
The similarities between the two presidents' instincts has become clearer since Mr Trump sacked the bellicose John Bolton as his national security adviser in September. The crucial disagreements between Mr Trump and Mr Bolton concerned the president's eagerness to pursue negotiations with Iran, North Korea and the Taliban in Afghanistan. The hawkish Mr Bolton was appalled. But Mr Trump is determined to press ahead. The result is that, after his warlike "fire and fury" phase, Mr Trump is now pursuing a diplomacy-first strategy that is strongly reminiscent of Mr Obama.
Foreign policy caution inevitably leads to clashes with the blob - Mr Obama was attacked for “weakness” and Mr Trump has been lambasted for “isolationism”. The debate over Afghanistan illustrates the point. Both Mr Obama and Mr Trump came to office very sceptical of the case for continued military involvement. Both presidents were then persuaded to send more troops - only to start pulling them out again, later in their presidencies.
The story of two cancelled air strikes underlines their joint caution. Mr Obama's last-minute decision in 2013 to cancel a bombing raid on Syria, intended to punish President Bashar al-Assad for using chemical weapons, was widely denounced by the Washington establishment. When Mr Trump ordered some air strikes on Assad regime targets in 2018, in response to another chemical attack, he got bipartisan praise in Washington for correcting Mr Obama's "error".
But these raids were just one-off gestures that did nothing to change the trajectory of the war in Syria. More recently, Mr Trump also made a last-minute decision to ignore his advisers and cancel an air strike, this time on Iran, after balking at the likely level of casualties.
Mr Trump’s reluctance to attack Iran was significant. It underlines the fact that his tough-guy rhetoric disguises a strong preference for diplomacy over force. The fact that Mr Trump and Mr Obama arrived at similar policies of pullback from the Middle East is crucial - given that the region has long dominated US foreign policy.
On other issues, however, there are important differences between the two presidents. Mr Obama believed in the importance of international agreements, while Mr Trump is highly sceptical of them. He has pulled the US out of the Paris climate treaty and a host of other international accords.
The Trump administration’s ardent protectionism also represents a break not just with Mr Obama, but with every other US presidency since 1945. However, Mr Trump seems to be in tune with the spirit of the times. The leading candidates for the Democratic nomination are now also embracing protectionism and a more hostile attitude to China.
This bipartisan embrace of protectionism is the economic equivalent of the Obama-Trump convergence on pulling back from the Middle East. Both policies are products of a declining confidence in America’s ability to emerge triumphant in economic or military competition with foreign rivals. The result is the adoption of more defensive and inward-looking policies.
Since the Trump and Obama camps revile each other, it remains a political and psychological necessity for both sides to ignore any convergence between their foreign policies. But when historians look back at the two presidencies, they will surely notice the underlying continuities. In their very different ways, both Mr Obama and Mr Trump have reduced America’s global commitments - and adjusted the US to a more modest international role.
Gideon Rachman is a columnist with the Financial Times