(CNN) A commander in chief who prizes nuance and restraint put his legacy in the war on terror Tuesday in the hands of a brassy successor who embodies gut-check leadership.

Forty-five days before the inauguration, Barack Obama and Donald Trump struck a contrast that not only reflected their chalk-and-cheese political styles, but their radically different doctrines for how best to keep America safe.

Obama traveled to MacDill Air Force Base in Florida to bid a poignant farewell to his troops. He offered one of his characteristic, professorial examinations of his own motives, place in history and responses to the threat from terrorism that has evolved but hardly waned during his eight years in office.

At almost the same time, the President-elect stood beaming in the cabin of his personal 757 alongside James Mattis, the retired general he will formally unveil later Tuesday in North Carolina as his pick for defense secretary and whom Trump delights in calling by his nickname, "Mad Dog."

More comfortable with an explosive tweet and a swipe at what he considers to be the Obama administration's fecklessness on terrorism than public self-examination, Trump has promised to break Obama's mold when he enters the White House.

But the outgoing commander in chief made the case that his successor should adopt many of his approaches and issued a forceful, implicit appeal to Trump to keep the fight against terror in what he sees as its proper perspective.

"The whole objective of these terrorists is to scare us into changing the nature of who we are and our democracy," Obama told the troops, without mentioning Trump by name.

"The fact is, people and nations do not make good decisions when they are driven by fear," he said, in an apparent plea to Trump not to embrace tactics used by the George W. Bush administration that much of his own presidency was dedicated to overturning and outlawing.

In his last major national security address, Obama argued that he had placed the US anti-terror campaign on more sustainable ground, morally, legally and militarily than it was on when he took office in January 2009.

In defending his decision to ban interrogation methods critics label torture, his efforts to close the prison at Guantanamo Bay and his withdrawal from Middle East battlefields, the President appeared to be directly addressing his successor: "Right makes might, not the other way around."

Obama said he was indeed right to pull troops out of Iraq and to end combat in Afghanistan, to forge a nuclear deal with Iran and celebrated the operation that killed Osama bin Laden.

Eying Republicans who blame him for the rise of ISIS, Obama touted the success of the US-backed offensive against the terror group in Iraq and Syria and argued he had mandated greater transparency on the way America uses drones.

While he pointed out that there had been no attack on the scale of the September 11, 2001, terror attacks during his tenure, Obama acknowledged the new wave of radicalized homegrown terrorists inspired by ISIS like those in San Bernardino, California, or Orlando, Florida.

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Leaving power means that Obama has no idea -- or control -- over whether those who come after him will build on the foundation he believes he has left.

Trump lashed Obama's approach as "disastrous" on the campaign trail, and vowed to launch an all-encompassing struggle reminiscent of the generations-long duel between the West and Communism.

He is already promising a more aggressive leadership style, and set the tone with his pick of Mattis. The general is regarded as a cultured and learned man by some of his former subordinates, but the President-elect has fixated on his nickname and history of military derring-do.

"He lead an assault battalion in Operation Desert Storm ... that's the way you're supposed to lead it," Trump said at the North Carolina rally.

"There was no games. Mad Dog plays no games."

The President-elect plans to crack down on Muslim immigration, to intensify the fight against ISIS and has threatened to bring back waterboarding -- although there are signs he may have backed off that promise after meeting Mattis.

Trump, without revealing his plans, has vowed to be far more aggressive in combating terror and has warned he will renegotiate Obama's nuclear deal with Iran.

On the face of it, Trump's fixation with strength and his own ferocious rhetoric -- as well as the appointment of vehement Obama critic, retired Gen. Michael Flynn, as his national security adviser -- suggests an immediate change of course.

And yet, the world often looks different from inside the Oval Office, and despite the clear temperamental and rhetorical gulf between the two men, it remains unclear how much of the Obama legacy Trump will tear down.

It could turn out Trump will decide that the combination of drone strikes, the scalpel of special forces raids and using local forces to combat ISIS -- policies Obama has pursued -- are the most effective options.

And new legal constraints introduced over the Obama years on interrogations of terror suspects combined with the political and military constraints imposed by years of grueling foreign wars might all combine to box Trump in.

"There is no question that President Obama was determined to make the US counter-terrorism policy sustainable -- not only in terms of the resources that we were putting into it but sustainable in terms of the legal basis in which we had been operating," said Derek Chollet, who served as a senior official in the Obama Pentagon and White House.

Chollet added that one reason Obama gave the speech Tuesday was to explain what he had done, to defend it and to show why going after terrorists in line with the rule of law was the preferable path.

"There is a lot that Donald Trump personally, or those around him, have said that would very much go against what President Obama has been talking about," he noted. "But like on every other policy issue, we are not going to really know what direction this is going to take until Donald Trump takes office."