But in style and tone, the vice-presidential debate was distinctly different.
Cheney and Edwards were seated casually, almost side by side -- rather than standing formally at lecterns as Bush and Kerry had been.
And the vice-presidential challengers were far more combative, exchanging pointed criticisms and staunchly defending their running mates.
Cheney began the 90-minute debate by rebuffing suggestions that the administration had mishandled the war in Iraq -- a critical issue for American voters.
"What we did in Iraq was exactly the right thing to do. If I had to recommend it all over again, I'd recommend exactly the right -- same course of action. The world is far safer today because Saddam Hussein is in jail, his government's no longer in power, and we did exactly the right thing," Cheney said.
Edwards responded sharply, "Mr. Vice President, you are still not being straight with the American people."
He went on to describe a bleak picture of the situation in Iraq and said, if elected, he and John Kerry would work to improve a war hampered by low U.S. troop levels and too few foreign allies.
"We need a fresh start. We need a president who will speed up the training of the Iraqi [forces], get more staff in for doing that. We need to speed up the reconstruction, so the Iraqis see some tangible benefit. We need a new president who has the credibility, which John Kerry has, to bring others into this effort," Edwards said.
Observers generally concluded that Kerry emerged the stronger candidate following last week's debate with Bush, who at times looked angry and flustered.
But Cheney remained even-tempered throughout the debate, often adopting the tone of a sage elder statesman and pointing disapprovingly to the political inexperience of his rival.
Edwards, who is 51, is serving his first term as a U.S. senator. But the vice-presidential candidate, who built a successful career as a courtroom lawyer, did not appear intimidated by the criticism of his 63-year-old opponent.
Citing statistics showing the United States has lost more jobs under Bush than in any time since the Great Depression of the 1930s, Edwards said: "I don't think the country can take four more years of this kind of experience."
The debate also turned to the question of Iran -- famously included in Bush's "axis of evil" speech three years ago. Cheney defended the continuation of U.S. sanctions against the Islamic Republic.
"We dealt with Iran differently than we have Iraq, partly because Iran has not yet, as Iraq did, violated 12 years of resolutions by the UN Security Council. We're working with the Brits and the Germans and the French, who've been negotiating with the Iranians. We recently were actively involved in a meeting of the board of governors of the International Atomic Energy Agency, and as I say, there will be a follow-up meeting in November to determine whether or not Iran's living up to their commitments and obligations. And if they aren't, my guess is, then the board of governors will recommend sending the whole matter to the UN Security Council for the application of international sanctions, which I think would be exactly the right way to go," Cheney said.
Both candidates also discussed the continued unrest in the Middle East, where more than 70 Palestinians have died in a week-long operation aimed at ending Palestinian rocket attacks on Israeli towns and settlements.
Edwards described the Bush administration as being "largely absent" from the peacemaking process. He also went on to cite other instances -- most notably in the global fight against HIV/AIDS -- where the United States must honor its responsibilities abroad.
"The AIDS epidemic in Africa, which is killing millions and millions of people -- it's a frightening thing, not just for the people of Africa, but also for the rest of the world. That, combined with the genocide that we're now seeing in Sudan, are two huge moral issues for the United States of America, which John Kerry spoke about eloquently last Thursday night," Edwards said.
Presidential contenders Bush and Kerry are due to hold the second of three debates on 8 October in St. Louis, Missouri. The third and final debate will be held on 13 October in Tempe, Arizona. Elections are on 2 November.