The debate centred around the Coalition's list of cuts and savings released today by Mr Hockey after weeks of pressure to do so by Labor.
The Coalition says it's found more than $36-billion to pay for its promises but Mr Bowen says he doesn't believe the numbers.
Joe Hockey has laid out the bulk of his costings, saying under a Coalition government there would be no cuts to health or education, and no changes to the GST.
He says he has identified $31.6-billion in savings to pay for most of the Coalition's election promises.
Mr Hockey says the biggest budget saving would be reducing the public service by 12,000 people, saving $5.2-billion over the next four years.
He says discontinuing business compensation measures from abolishing the carbon tax will save just over $5-billion, while there would also be savings from scrapping the minerals resource rent tax.
Mr Hockey says a Coalition government would pay off the national debt that will cripple the Australian economy if it's not dealt with.
"Mr Bowen said debt is okay. If debt is the problem more debt is not the answer. You have to live within your means. Today I have outlined $31-billion of cuts. and I have done that on the basis that so much of what Labor has spent over the last few years has been waste. The challenge is that each year we need to find ten to twelve billion dollars a year just to fund the interest on Labor's debate. That's the equivalent of ten new teaching hospitals every year."
The Coalition says abolishing the schoolkids bonus would save $4.6-billion, and delaying increasing the compulsory superannuation guarantee would save $1.6 billion.
The costings say the Coalition's proposed 1.5 per cent company tax levy, which exempts small businesses, would raise $4.4-billion towards funding the paid parental leave scheme in its first two years.
Mr Bowen says the announced cuts don't cover all the promises made by the Coalition and a $70-billion budget shortfall that Labor has been predicting remains true.
"So there is a very substantial black hole in Mr Hockey's numbers. We believe it to be $70 billion. We agree with his figure. We agree with his figure. But if it's not $70 billion he could clear it up by telling us what it is. By releasing his full budget impact. He could clear it up now at this podium by releasing, not only a table of costings, but his full impact on an underlying cash balance basis on the budget."
Both men were quizzed on when the budget could be expected to return to surplus.
Mr Bowen says a re-elected Labor government would aim to return the budget to the black in 2016-17.
But Mr Hockey has again refused to set a date, saying a Coalition government would return the budget back to health when it's responsible to do so.
And both men say the other can't be believed.
"(Hockey): Well dejavu here I am again! Another Labor Treasurer saying they are going to deliver a surplus in the next term of government. Hogwash. Labor will never deliver a surplus. Its not in their DNA. They never will. Only the coalition can deliver a surplus. (Bowen): A lot of huff, a lot of puff, a lot of bluster, a lot of blowing. No date."
Chris Bowen says Labor is seeking a mandate from voters to continue its plan to build a better Australia, and to keep the economy strong.
Mr Bowen says the economy is 14 per cent bigger than when Labor came to office in 2007, and would continue to grow.
Mr Hockey says the Coalition should win government because it has a sensible plan.
He says this is to pay down debt, reduce waste and taxes, boost productivity, cut red tape, move workplace relations to what he calls the "sensible centre", and secure new trade deals with Asian nations.
