It may not really matter who won Tuesday night’s vice-presidential debate; voters are seldom influenced by who’s No. 2 on the ticket. (There’s a reason this is called a presidential election. )

And yet each high-profile debate helps clarify the choices before the voters. Tuesday night’s certainly did. Perhaps because the contrast between the two debaters was so clear. There’s no doubt which candidate was more stylish, youthful, charismatic, smooth, photogenic, smiley-faced . . . . It was John Edwards, and, on my highly personal scorecard, all those are just more reasons why he lost this encounter.

Because we’re electing a vice president of the United States, not a young charmer. Besides, Senator Edwards’ charm, like his smile, has a certain pasted-on quality. As if he’d wandered into this televised debate out of a toothpaste commercial.

Nobody would ever accuse Dick Cheney of being charming. Competent, cogent, knowledgeable, experienced, dry, tough, direct or even abrupt . . . the vice president is all of those. But charming? stylish? No way. He’s the brains of the outfit, not the star of the production.

Mr. Cheney seems the perfect fit for the office of vice president: a team player with no further political ambitions of his own, someone fully prepared to step into the president’s role if he had to, and a man not given to suffering fools. Or even mediocre opponents.

It may be hard to recall now, but it was John Edwards who took the offensive from the opening bell. Because it was Dick Cheney’s counterpunches that struck home:

He recounted John Kerry’s 20-year Senate record of voting against defense measures – a record that spans the Cold War, the first Gulf War, and now the war in Iraq – with devastating effect. And he wasn’t any softer on John Edwards’ record as an absentee senator, especially as a member of the Senate Intelligence Committee.

John Edwards is so light a presence in the U.S. Senate that the vice president couldn’t even remember meeting him.

And when John Edwards pointed out how badly things were going in Iraq, the vice president noted that Senator Edwards had said the situation in Afghanistan was deteriorating, too, before things turned around on that front.

The vice president also recalled visiting El Salvador years ago to observe elections in the middle of a long, cruel war. Things looked bleak there, too, before elections were held and things turned around.

In the country’s current crisis, which began September 11, 2001, and continues indefinitely, Dick Cheney represents constancy of purpose – whatever the news from Iraq on any given day. Constancy of purpose is not exactly the strong point of either candidate on the Democratic ticket, with their shifting votes and wildly inconsistent stands on the war in Iraq and against terror.

How is a presidential candidate who’s called our allies “a coalition of the bribed and coerced” going to lead that coalition, let alone expand it? How’s he going to work with the courageous new Iraqi premier he’s dismissed and demeaned as some kind of American puppet who lacks all credibility?

That’s the kind of thing you don’t say even if you believe it. Especially if you believe it. Remember how both FDR and Churchill treated de Gaulle at those wartime conferences? With outward respect, even though both thought of him as an arrogant pain.

The most unconvincing statement John Edwards made all night was his claim that he’d been “completely consistent about Iraq . . . .” Again and again the vice president cited Senator Edwards’ own record against him: “Whatever the political pressures of the moment requires, that’s where you’re at.”

A telling moment came when Dick Cheney noted that, when John Kerry seemed to be losing the anti-war vote to Howard Dean in the Democratic primaries, Senator Kerry chose to vote against funding the war. So did John Edwards. “Now, if they couldn’t stand up to the pressures that Howard Dean represented,” Mr. Cheney asked, “how can we expect them to stand up to al-Qaida?”

To all of which Senator Edwards could only respond by crying (ITALICS) Halliburton! Class warfare has become the last refuge of demagogues in this election season, whether it’s being waged by a scruffy Michael Moore or a glossy-smooth John Edwards.

It would take more than 90 seconds to explain that the vice president severed any real connection to Halliburton when he took his oath of office, and to go into the mixed record of that giant, indispensable civilian arm of the military over the years. A government investigation did clear Dick Cheney of any wrongdoing while he was Halliburton’s CEO, and even praised him for his cooperation with the Securities and Exchange Commission. As for Halliburton’s bad record in Libya that John Edwards mentioned, it was compiled before Mr. Cheney joined the company in 1995.

But it would take so long to answer all the false charges that John Edwards fired off in a second or two that the vice president just shrugged and recommended that voters go to FactCheck.org. Some smears are so thick they’re beyond snappy comebacks.

It’s not who won the battle of the sound bites Tuesday evening that will matter, but who can lead – even in a difficult time to lead.

In a now distant but not so different time in American history, a stylish senator named Stephen A. Douglas was poised to become the next president of the United States. A master of the rhetorical flourish, this prince of the Democratic Party never saw a crisis that couldn’t be sidestepped, a hard choice that couldn’t be postponed, or an evil that couldn’t be skipped over lightly.

It was Senator Douglas’ unprepossessing Republican opponent – a tall, gawky figure, homely beyond reason – who spoke of hard decisions that could not be avoided, of sacrifices that would have to be made. Strangely enough, it was Mr. Lincoln’s warnings that would in the end get through to the American people, and save the Union.

Tuesday night, it was Dick Cheney who warned Americans that we are now facing a shadowy enemy unlike any we have known before, an enemy that has already attacked us with disastrous results. And regimes that harbor terror have made themselves our enemy, too. The best way to protect ourselves, the vice president asserted, is to confront them and if necessary change them. Or we can choose to temporize and drift, and wait for the next assault.

“We were attacked,” John Edwards conceded at one point, “but we weren’t attacked by Saddam Hussein!” He still hasn’t connected the dots. He is still making fine distinctions between different terrorists as though they aren’t all united in their hatred of all that America and the West itself represent in the world. Whatever their next target – a schoolhouse in Russia, a bus in Jerusalem, a skyscraper in New York – they’re all in it together. And one way or another, all of them will have to be overcome. The war in Iraq, like the one in Afghanistan, is just another front in the same war. And we cannot prevail in what is a world war if we refuse to recognize that we’re in one.