Clinton, a 60-year-old New York senator who is aiming to become the first woman US president, said Republican candidates for the White House contenders were offering "more of the same".
"Just by looking at us, you can tell we aren't more of the same... We will change our country," she said.
The debate is the final meeting ahead of Tuesday's Democratic primaries in 22 states.
The so-called "Super Tuesday" is set to be the biggest single day of voting in US presidential nominating history.
Clinton and Obama have each taken two of the first four significant nominating contests in the race to be the Democratic contender in November's election.
Both candidates levelled criticism at John McCain, who so far is leading the race for the Republican nomination.
They attacked his comment that US troops could remain in Iraq for 100 years and his support for extending tax cuts by George Bush, US president, after voting against them at the time.
"Somewhere along the line, the [McCain] Straight-Talk Express lost some wheels and now he is in favour of extending Bush tax cuts that went to some of the wealthiest Americans who don't need them and we're not even asking for them," Obama said.
Clinton, asked about the prospect of another term in the White House for a Clinton after eight years of her husband, said she hoped to remedy what she called damage caused by Bush.
"It did take a Clinton to clean after the first Bush and I think it might take another one to clean up after the second Bush," she said.
The debate was the first to feature Obama and Clinton since a bitter exchange between the two in South Carolina last week.
A series of personal attacks between the two senators sparked a week of bitter accusations by Obama, Clinton and her husband, Bill.
But the tone of the debate at Los Angeles' Kodak theatre was a good deal more positive.
Obama, an early opponent of the Iraq war, questioned Clinton's 2002 senate vote to authorise the war in Iraq.
|The two candidates had clashed in the run-up |
to the South Carolina primary [AFP]
"Part of the argument that I'm making in this campaign is that it is important to be right on day one," he said.
Meanwhile, Clinton criticised Obama's plan on healthcare provision because it could leave up to 15 million people uninsured.
"You have to bite this bullet, you have to say 'Yes, we will try to get to universal healthcare'," she said.
Obama, who is aiming to become the first black US president, said anyone who wanted healthcare could get it under his plan, which would focus on bringing down costs.
Obama and Clinton also disagreed on whether illegal immigrants should have the right to driver's licences, with Clinton opposing the idea.
The debate was their first since Obama crushed Clinton and Edwards in a South Carolina landslide on Saturday.
In the Republican race, McCain's bid for the White House was boosted on Thursday when Arnold Schwarzenegger, Republican governor for California, endorsed him.
"He is a great American hero and an extraordinary leader. This is why I am endorsing him to be our next president of the United States," he said.