Tory leader David Cameron says the government's proposed rescue package for Northern Rock is a "sub-prime deal from a sub-prime minister".
Cameron says Brown 'synonymous with delay and dithering'.
In Commons exchanges, he said Gordon Brown was like "a used car salesman who won't tell you the price"; after he asked what the total cost would be.
Mr Brown accused the Tories of "flip flopping between nationalisation, private sales and administration".
But Mr Cameron hit back that the deal was "damaging" and "dodgy".
The heated exchanges came after the government announced plans to turn Northern Rock's £25bn Bank of England loan to the stricken bank into bonds and sell them to investors.
The bonds would be guaranteed by the government to speed up a private sale.
If a private sale is not reached, the bank will come under temporary public ownership.
But Mr Cameron said taxpayers had a right to know what their total exposure was under the government's plans for the troubled bank - before adding that he believed it was £55bn.
He taunted Mr Brown that the Northern Rock deal was "as much a rescue package for your reputation".
"It's like a used car salesman who won't tell you the price, won't tell you the mileage, won't give you a warranty," he said.
"You've gone from prudence to Del Boy without even touching the ground.
"The fact that you won't answer a single question just shows what a dodgy deal this is."
He also accused the prime minister of "bad judgment" for flying to China with Sir Richard Branson, one of the principal bidders for Northern Rock.
But Mr Brown described the comments as "the height of opportunism from the Conservative Party. One day they favour nationalisation, another day they favour a private sale."
Lib Dem leader Nick Clegg asked the prime minister how he could "justify fleecing the taxpayer by handing a blank cheque to the private sector when you know, unlike the Conservatives, that temporary nationalisation is the right thing to do".
Mr Brown said the government plans would protect the interests of the taxpayer "in the best possible way".
Earlier, in an interview with The Times, Mr Cameron described Mr Brown as "that strange man in Downing Street" and accused him of playing politics with anti-terror measures.
Heated exchanges expected
He said his support for extending the period that terrorism suspects can be held without charge for up to 42 days - a move opposed by Tories, Lib Dems and some Labour MPs - was an attempt to "make the Tories look soft on terror".
"That is my problem with our prime minister: he looks at every single issue from the point of view of what is the right dividing line that divides me from my opponent, not what is right for the country, and I think that is what he is doing here," he said.
Home Secretary Jacqui Smith is set to unveil the controversial Counter-Terrorism Bill on Thursday.
It is likely to spark heated exchanges during its second reading debate in the Commons in a few weeks time.
Asked if was sticking with his pledge to match Labour spending plans to 2011, Mr Cameron said: "I am being very careful because if you say anything else that strange man in Downing Street will cook up an enormous package of Tory spending cuts."
Mr Cameron, who is set to address the World Economic Forum in Davos, Switzerland, on Wednesday, also criticised Mr Brown for being unprepared to deal with the economic downturn.
"We have not fixed the roof when the sun was shining," he said.