Mr Brown defended his so-called "golden rules" - which state the government should only borrow to invest over an economic cycle not to fund current spending and public sector debt must remain below 40% of national income - against attacks from Mr Cameron.
The Tory leader said the rules had "failed to deliver responsibility in the good years and as the bad times came they have collapsed completely".
But Mr Brown said borrowing levels under Labour were lower than under the last Conservative government.
"We have met our fiscal rules in the last 10 years," he said.
"They broke the roof. We fixed it."
The two leaders also argued over how to best support the economy to prevent the current downturn from doing lasting damage.
Having excited his party with talk of a new Keynesian economic policy, Mr Darling is now trying to reassure the markets that our old friend Prudence is just sleeping - and is not actually dead
Mr Cameron said the prime minister had been "caught red-handed" making "irresponsible" claims about government plans to spend its way out of the current problems.
But Mr Brown said the Tories had no consistent approach to helping minimise the impact of the economic slowdown.
"We have to spend in a way which takes us through this economic crisis," Mr Brown said.
Mr Darling will say later on Wednesday that the government's fiscal policy must adapt to the current exceptional economic circumstances.
"Just as markets change, so should policy," he will say.
"Today, governments all over the world are using approaches that had until recently been consigned to policy making history, but it is natural that the conduct of policy should evolve," Mr Darling will add.
"Three weeks ago, we worked with other countries to put in place a plan to stabilise the banking system.
Mr Darling will deliver his speech at a meeting in London
"These countries are committed to working together to strengthen supervision in the global financial system.
"And today we need the same determination to support the wider economy. To ensure that fiscal policy supports monetary policy, here and across the world, in these exceptional circumstances."
Shadow chancellor George Osborne has said the scrapping of the fiscal rules would destroy "the final remaining pillar" of the prime minister's economic legacy.
He has warned that any "spending splurge" would further damage Britain's economic outlook and reduce the opportunity for interest rate cuts which he says are needed to stimulate demand.
'Out of control'
The Tories have claimed that borrowing levels - which totalled £37.6bn between April and September - are already "out of control".
They maintain that further increases in borrowing would not be a panacea for the economy but a reflection of the chancellor's need to plug a widening gap in his finances with tax revenues falling and unemployment costs rising.
While accepting that it may be "necessary" to borrow more in an economic downturn, the Lib Dems have said the government must demonstrate it has a plan to rebalance the public finances once the economy starts growing again.
It is entirely wrong for the government to assume that the economy should be stimulated by yet more public spending rather than tax cuts
Vince Cable, Lib Dem treasury spokesman
The party's treasury spokesman Vince Cable said Labour's fiscal rules had already "lost much of their credibility" and Mr Darling must now admit they have been broken.
"During a recession it is inevitable that the budget deficit will increase," he said.
"However, it is entirely wrong for the government to assume that the economy should be stimulated by yet more public spending rather than tax cuts, particularly for the low paid."
The BBC's political editor Nick Robinson said that while Mr Darling may quietly concede that the fiscal rules are at an end, he will say a future framework for borrowing and debt levels will still be responsible.
Battle over Keynes
Suggestions the government will bring forward large public works projects to support spending and employment during the downturn have been criticised by some experts.
A group of leading economists have described this "Keynesian" philosophy - named after the economist John Maynard Keynes - as "misguided and discredited" amid concerns it could harm the private sector which they believe should lead the economy recovery.
Mr Darling would seek to "pour a little cold water" on talk of a full return to Keynesian economics, the BBC's Nick Robinson added.
He will point out that the economist argued that spending should not be cut in a downturn, not that it should be allowed to "let rip".
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