Back last summer, John F. Kerry made an observation that struck him and his partisans as so self-evidently true it could hardly be disputed. The Democratic nominee said the U.S. intervention in Iraq so far has done more to recruit terrorists than to defeat them.

President Bush reacted with a disdain and disbelief that no one who heard it could doubt was genuine. "I don't think they need an excuse for their hatred and their evil hearts. You do not create terrorists by fighting back; you defeat the terrorists by fighting back."

There, in that exchange, was the 2004 election in miniature. There are two leaders who agree the world is a dangerous place, but disagree radically about the nature of history's test and the brand of leadership it demands. A mind that sees complexities and unintended consequences? Or one that understands the primitive nature of a new war, and is prepared to match the enemy's determination with his own?

Opposing instincts about the nature of leadership -- more than any specific point on either candidate's agenda -- has been what all the shouting has been about in the loud and angry campaign now coming to a close, as many strategists and students of the presidency see it. There are certainly sharp policy choices, but on the big issues they are differences of detail -- who could be "more effective" in managing the Iraq turmoil? Across-the-board tax cuts or targeted ones? -- that by themselves can hardly explain the chasm that has divided Americans this year.

The choice confronting voters Tuesday is as much psychological as ideological. The balloting will amount to a great national Rorschach test, with people looking at two starkly different styles of leader and responding in visceral ways about what intellectual and character traits they value in a wartime president, and what balance of force vs. persuasion they seek as the United States relates to its neighbors on an anxious planet.

"The basic fault line in this election is leadership psychology," said Stanley Renshon, a political scientist and psychologist who has written biographies of President Bush and his immediate predecessor, Bill Clinton.

The result is a campaign in which the people on different sides of the fault line seem to be living in alternate realities, unable to agree on even basic facts. One group perceives Bush as one of the great visionaries of recent U.S. history, another as one of its most extravagant failures.

At every turn in this campaign, Bush has presented leadership as, above all, a matter of conviction, in which the hard part of governance is not deciding right from wrong but pursuing right in the face of setback and criticism. And so his closing argument in the final days of this campaign: "Americans have learned that even when you disagree with me, at least you know what I believe and where I stand."

At every turn in this campaign, Kerry has presented leadership as above all a matter of judgment, in which governance is indeed a challenge of discerning the right choices in an interlocking world that can not be navigated by slogans or a single-minded focus on one problem. And so one of the Massachusetts senator's favorite lines, as he at once raps Bush for simple-mindedness and for neglecting mounting problems at home: "A president has to be able to do more than one thing at the same time."

David Gergen, a writer and political commentator who worked for Clinton as well as a succession of Republican presidents, said American politics has rarely offered such a stark contrast in leadership models. The choice, he said, is "between fact-based versus intuition-based policies." Confronted with a policy decision, Gergen believes, Kerry's instinct is to study and seek to master the complexities of his choice; Bush's instinct is to act quickly, in the belief that a leader is better off to drive events and circumstances rather than be driven by them.

Bush's tenure, as Gergen sees it, has been a case study about both the advantages and hazards of this approach. Before Sept. 11, 2001, Bush brushed aside expectations that he would govern modestly as a result of his weak mandate in the 2000 election, and instead moved boldly to enact deep tax cuts. After the terrorist attacks, his confident declarations of victory and moves to refashion national security around a doctrine of preempting threats is one reason a majority still trusts him more on the issue of terrorism.

The question to be answered Tuesday is whether this support is deep enough to offset the political price that will come from the troubled intervention in Iraq, which Gergen predicted will be studied by future historians as "a classic case study" in flawed decision making and planning.

The vivid contrast offered by Bush and Kerry is in many ways a recognizable one for students of leadership. In 1953, British philosopher Isaiah Berlin wrote an essay, "The Hedgehog and the Fox," that has been studied for years by historians. Playing off an ancient Greek proverb, which held that "the fox knows many things, but the hedgehog knows one big thing," Berlin wrote that most people gravitate by instinct and habits of mind to one style or the other.

As refined by political scientists, Berlin's thesis divides leaders into those driven more by ideology, and who value clarity above all, and those who govern more by analysis and improvisation, who value flexibility in the face of changing facts and circumstances. By this light, the essay anticipated by 50 years the choice of Bush vs. Kerry. The president since 2001 has framed almost every policy choice, even on the domestic front, in the context of the fight against terrorism. He has warned other nations that they are "either for us, or against us," and has mocked Kerry's addiction to "nuance." For his part, Kerry has sought to rebut the notion that he is a "flip-flopper" while also arguing that a sophisticated approach is an asset for a president.

"Now I know that there are those who criticize me for seeing complexities," he acknowledged in his acceptance speech at the Democratic National Convention. "And I do, because some issues just aren't all that simple."

Bush and Kerry, according to some scholars of leadership, both have a rhetorical problem: Their style of speaking often highlights the defects rather than the advantages of their different approaches.

James MacGregor Burns, a presidential biographer and the namesake for the Burns Academy of Leadership at the University of Maryland, said many of the successful presidents, including Franklin D. Roosevelt, have been improvisers. But Kerry, unlike Roosevelt, has not been able to articulate that his occasional shifts rest on a "set of broader principles," he said.

The result is what Burns regards as an unfair perception that Kerry is motivated by "expediency and shiftiness."

Renshon believes that Bush suffers from the same problem in reverse. The biographer strongly rejects the view held by many Bush critics that the president is simply not very intelligent, but acknowledges that he is not drawn naturally to the details of policy in the fashion of Clinton or Kerry.

Bush is "much more interested in leadership than governing," Renshon said. But he speaks in a staccato style that sometimes relies on stock phrases. "He does not articulate his premises well," Renshon said.

The great surprise of the Bush years, perhaps, is how ideologically charged this national argument over leadership and war has become. After a long and sullen campaign, and years of hearing commentators talk about "red" and "blue" America, it is easy to forget how recently most analysts assumed that American politics had entered an age of consensus. Clinton was personally controversial, but for most of his presidency his centrist policies commanded support levels of 60 and 70 percent in polls. Bush himself, after Sept. 11, enjoyed approval ratings of 90 percent or more. Historically, war has more often united Americans behind presidents.

Bush shattered the consensus by prosecuting a war against Saddam Hussein's Iraq that flowed directly from a leadership style that valued action above all and brushed aside the warnings of skeptics. A war that was controversial when it began became only more so as its main assumptions -- about the presence of weapons of mass destruction, and the difficulty of the post-invasion phase -- were undermined by events. Kerry took a nuanced but sometimes confusing middle ground, saying he supported confronting Iraq, but not a "rush to war" without a "plan to win the peace."

Not surprisingly, this has left the closing days of the campaign as a continuation of a national debate that has echoed for nearly two years.

Kerry last week in Florida was lambasting a "president who's unwilling to admit the mistakes he has made, and says he would do everything all over again exactly the same."

Bush in Ohio was assailing his challenger as a man who "has taken a lot of different positions, but he rarely takes a stand."

Democratic candidate John F. Kerry: "A president has to be able to do more than one thing at the same time."

President Bush: "Even when you disagree with me, at least you know what I believe and where I stand."