FORTUNE — When historians rank presidents, Abraham Lincoln usually comes in first, while Thomas Jefferson is nearly always in the top five. Each left a legacy worthy of celebration on Presidents’ Day, but they did so in radically different ways.
Jefferson was as prepared for the presidency as anyone has ever been. He had been a key member of the Continental Congress, ambassador to France, governor of Virginia, secretary of state, and vice president. When he took office in 1801, Americans knew exactly what they were getting. Jefferson’s abundant gifts unsurprisingly produced a successful presidency, but one that was regarded as extraordinary largely because of the Louisiana Purchase.
Lincoln, on the other hand, was among the least prepared to become president of anyone ever elected to the White House. His national political career included only one term in Congress. He was chosen as the Republican nominee over former New York governor and U.S. senator William Henry Seward, the front-runner, largely because his abbreviated record allowed him to position himself as the least anti-slavery — and therefore most moderate — Republican. Once in office, however, Lincoln revealed himself to be considerably more dedicated to opposing slavery and maintaining the Union at any price than Seward was, and his political and strategic genius was a crucial component in the Union’s Civil War victory.
It’s hard to imagine two more different routes to great presidencies. What’s more, these paths shaped what they did in the White House. Granted, the Louisiana Purchase was a great achievement, but it would have happened even without Jefferson. If he had not been president, it is likely that either John Adams or James Madison would have been when Napoleon proposed selling the Louisiana territory. Both supported the purchase, and both would have been able to execute it.
Jefferson was president of a country whose system for selecting leaders was working very well at the time. Who would object to four leaders in a row of the quality of Washington, Adams, Jefferson, and Madison? Under those conditions, a known quantity — an insider, in today’s terminology — is by far the best bet.
Lincoln is another story altogether. Without him, the Civil War would have turned out very differently. When the South Carolina militia besieged Fort Sumter, Seward, his secretary of state, wanted to yield it peacefully, believing that the South would return to the Union within months. It was Lincoln’s idea to send supplies to the beleaguered fort — a tactic that goaded Southern forces into firing the first shots of the Civil War. Those shots united the North, which had been on the fence over fighting.
When Lincoln became president, the American political system wasn’t working. The nation was on the brink of collapse, and everyday politics had produced a series of presidents who aspired to mediocrity and failed even at that. Who would want to be led by Millard Fillmore, Franklin Pierce, or James Buchanan? In the midst of crisis, an outsider — someone who could make the daring choices that no one else would make — was the only option.
Inherent in picking an unknown, though, is risk. Not all unknowns are successes. Woodrow Wilson’s political resume was even shorter than Lincoln’s. His racism was a disaster for civil rights, while his rigidity led to the United States’ failure to enter the League of Nations, leaving the United States to play no role in countering the rise of Germany in the 1930s.
What’s true for a country is true for a company as well. If you have a successful enterprise with a well-functioning, detailed system for selecting leaders — GE (GE) is the classic example — then picking a known quantity is standard operating procedure. You probably won’t get a Lincolnesque genius, but you will almost certainly get someone who, even if they are replaceable, will do the job well. But if a company is in turmoil, or the environment is changing rapidly, or the situation is so desperate that there seems no way out — as it was for IBM (ibm) when it hired former consultant and RJR Nabisco CEO Lou Gerstner to engineer a turnaround — then the unknown quantity is usually the best choice.
The leader who is willing to do what no one else would do is probably the only one capable of salvaging a bad situation, because doing business as usual is precisely what got the company in trouble in the first place. No one but Steve Jobs would have cancelled 70% of Apple’s products against the wishes of his handpicked board of directors. That decision helped make Apple (aapl) what it is today.
Sometimes companies and countries need to go with a known quantity, and sometimes they must roll the dice. More often than not, the American people have made the right call, producing Washingtons and Jeffersons, Lincolns and Roosevelts.
Gautam Mukunda is an assistant professor at Harvard Business School and author of Indispensable: When Leaders Really Matter (Harvard Business Review Press).