WASHINGTON >> She showed up with color-coded maps. He wrote long private memos. She argued for sending more troops to fight the enemy and help rebuild a country. He argued for a more targeted mission, a smaller deployment and a limit on how long they would stay.

In the end, neither Hillary Rodham Clinton nor Joe Biden prevailed during that momentous debate over Afghanistan in 2009 in the Situation Room. President Barack Obama opted to send 30,000 more troops, much as Clinton recommended, while setting a deadline for withdrawing them, much as Biden suggested.

The collision between Biden, the vice president, and Clinton, then the secretary of state, was hardly the only one that played out during the four years they served together in the Obama administration. Biden and Clinton represented the yin and the yang of Obama’s foreign policy, one encouraging the president’s own natural caution and the other giving voice to his more assertive side.

If Biden were to join the Democratic presidential race for the 2016 election, the contest between him and Clinton would in effect put on a public stage the struggles waged in the secrecy of the Situation Room. More so than on domestic policy, where their differences are narrower, the two former compatriots reflect the competing voices that have shaped Obama’s approach to the world and the poles that continue to divide the Democratic policy on national security.

"If he came in, it would change the nature of the debate," said Vali R. Nasr, who served under Clinton as a special adviser on Afghanistan and Pakistan and is now dean of the School of Advanced International Studies at Johns Hopkins University. "It would be much more a debate about these two fundamental approaches."

Time and again, Clinton and Biden faced off over the use of U.S. power in the world. Biden oversaw the withdrawal of troops from Iraq in 2011 while Clinton supported keeping a residual force behind. She argued for the military intervention that ultimately toppled Moammar Gadhafi in Libya while he opposed it.

He warned against the special forces raid into Pakistan that resulted in the death of Osama bin Laden, urging that they wait for more intelligence confirming his presence, while she recommended going forward with the operation. She was a prime advocate of arming and training opposition forces in Syria, a push he did not join. In recent days, she came out against Obama’s trade pact with Pacific nations, while the vice president endorsed it.

Put together, the disagreements underscore a broader philosophical schism over America’s role in the world a dozen years after the invasion of Iraq.

"He may be more cautious about the outcomes of the significant use of military force," said Barry Pavel, a national security official in the White House during Obama’s first term and now a vice president of the Atlantic Council, a Washington think tank. "She may be more robust in ensuring that U.S. engagement is felt in a meaningful way and there isn’t a perception of a U.S. withdrawal or disengagement."

Biden appears closer to the center of gravity among Democratic primary voters, who according to polls are deeply skeptical of U.S. military involvement abroad. In a New York Times/CBS News survey this year, 89 percent of Democrats described themselves as concerned that intervention in Iraq and Syria "will lead to a long and costly involvement there."

Sen. Bernie Sanders of Vermont, Clinton’s most potent challenger for the Democratic nomination, has appealed to that liberal base with a record significantly to the left of both hers and Biden’s, including voting against the Iraq War and the Patriot Act as well as opposing Obama’s surge in Afghanistan. Both Clinton and Biden voted for the Iraq War before eventually disavowing it.

Clinton and her advisers seem more focused on a general election audience, demonstrating that she would adopt a more assertive foreign policy than Obama. "They do not want Hillary to be seen as a left winger, and if Joe Biden wants that mantle, they’ll give it to him," said Leslie H. Gelb, president emeritus of the Council on Foreign Relations, who has advised Biden. "They’re not going to compete in these primaries as foreign policy liberals and leftists. They’re not going to do it."

It has not always been so. When they served in the Senate together, Clinton and Biden took relatively similar, center-left stances on national security and foreign policy. Biden has the longer record, tracing back to the 1970s when he supported arms control treaties with the Soviet Union through the 1990s when he backed intervention in the Balkans. As first lady, Clinton traveled the globe widely but largely stayed away from big foreign policy debates.

After the Sept. 11, 2001 terrorist attacks, Biden and Clinton came down in roughly the same place — for the Iraq invasion but later opposing President George W. Bush’s troop surge to finally put down insurgents. "If you look at their votes on wars or supporting guerrilla efforts by others, they voted almost exactly the same way," Gelb said. "The differences begin to occur in the Obama administration."

Biden seemed to emerge from the Iraq crucible with more scars and shifted more to the left. He was quicker to repudiate the war and, with Gelb, crafted a plan to essentially divide Iraq into three autonomous regions under a limited central government. Once he became vice president, he was determined to avoid what he saw as the mistakes of the previous administration.

Clinton resisted disavowing her original vote for the war for a long time and as secretary of state pressed for a muscular approach to the world. In effect, she and Biden competed for Obama’s foreign policy. It was not overtly hostile — the two would often have pre-meetings to hash out their positions before the main national security gatherings in the Situation Room. But once the debate began, neither was a shrinking figure. And aides said Obama encouraged Biden to play a devil’s advocate role, questioning the military especially.

At first, the president seemed to lean more toward Clinton’s view, if not entirely, as with the 2009 troop surge in Afghanistan. But the war in Libya in 2011 proved a turning point. After his reluctant approval of airstrikes left behind a fractured country, Obama soured even more on intervention.

With Clinton now gone from the administration, Biden seems to have won the battle to shape Obama’s thinking. Clinton is on the campaign trail arguing for a tougher approach to Russia’s intervention in Ukraine and the battle against the Islamic State in Syria.

Both would have episodes to cite from their time in the Situation Room if they were to face off. Clinton could point to Biden’s reluctance to authorize the operation that killed bin Laden — he worried about a repeat of President Jimmy Carter’s ill-fated attempt to rescue the hostages in Iran in 1980 and suggested waiting for more intelligence to be sure bin Laden really was at the compound in Pakistan. In his own telling, Biden said "don’t go," but he has revised his account to say he also eventually told Obama to follow his own instincts.

For his part, Biden could point to Libya as a case study in the perils of Clinton’s brand of U.S. meddling in the conflicts of other countries. She might argue that she favored a more expansive involvement than that taken by the administration, which all but washed its hands after Gadhafi’s death, but the terrorist attack on a diplomatic compound in Benghazi has become an enduring political liability for her.

Either way, it could be a profound debate for a party still struggling to define its post-Iraq approach to foreign policy. Clinton and Biden would take their running arguments from the Situation Room to the campaign trail and ask their fellow Democrats to decide who is right.

"They disagreed and they disagreed spiritedly," said one former administration official who was in the Situation Room but did not want to be named discussing private debates. "These are not shy people."

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