Clarke and Duncan Smith offered each other jobs
Mr Clarke said nobody was more Eurosceptic than his rival, who wanted to take Britain out of the European Union.
That claim was denied by Mr Duncan Smith, who argued Mr Clarke's difference with the majority of his party over Europe would be exploited by the Labour party.
The debate came after former prime minister John Major gave Mr Clarke his backing and delivered a stinging attack on the legacy of Lady Thatcher, who supports Iain Duncan Smith.
Euro warnings
In the live studio debate, both challengers agreed the Tories needed to get onto a broader agenda than the issue of Europe alone.
Although they ended by stressing the need for unity and pledging to fight together against Labour, their divisions were clear on that same issue.
Mr Duncan Smith said: "The only way we can settle this is by leading through the majority of the party who don't want to join the euro."
He argued his rival would have problems tackling Tony Blair after each inter-governmental conference.
"They'll tease this out every single time and we will break up this for four years," he continued, promising to tolerate the views of Tory pro-Europeans.
But Mr Clarke insisted he was no Euro-federalist and only wanted a more moderate approach to Europe.
"There is nobody in the party - except Bill Cash - who holds more europhobic views than Iain.
"He quotes in his literature someone who calls him 'an intelligent Europhobe' - a hater of Europe."
Public services focus
Both contenders offered the other jobs in their shadow cabinets, although Mr Clarke said he only wanted to return to the frontbenches as leader.
As they agreed on the need to press the Conservative message home to voters on public services, Mr Clarke and Mr Duncan Smith explained their views on education and health.
The shadow defence secretary argued there should be more voluntary and private provision in healthcare, as happened on the Continent.
"I think this debate is now too big for politicians to play stupid games about what people should and shouldn't have," he explained.
Mr Duncan Smith also advocated using credits to allow parents to move their children away from failing schools.
Having already underlined his experience in government, Mr Clarke said credits were not necessary.
Instead, he argued expanding better schools was the answer and said under Labour schools "almost get rewarded for failing".
On healthcare, he favoured more decentralisation and talking of giving back NHS staff "their professional pride".
He said the whole range of opinions would be represented in his shadow cabinet and pressed Mr Duncan Smith to allow his supporters to give their "honest opinion now" rather than waiting until the referendum campaign.
Returning to power
The debate was seen as relatively gentlemanly after the bitterness surrounding the interventions of two former Tory prime minister's in as many days.
Joining the fray on Tuesday, Mr Major said it was Mr Clarke who could win back floating voters.
The former prime minister said Mr Duncan Smith had voted "night after night" against his government over Europe before the 1997 general election.
Thatcher legacy
And he accused Lady Thatcher, who says Mr Clarke would steer the Tories to disaster, of actively encouraging young Tory MPs to vote against his government on Europe.
Mr Major later denied claims Mr Duncan Smith had been offered job in his government and had refused because of differences over Europe.
But Mr Duncan Smith insisted party whips had asked him to become parliamentary private secretary.
And Mr Clarke used the debate to blame government communications director Alastair Campbell for "rubbish" reports on claims of tobacco smuggling by British American Tobacco, of which he is a non-executive deputy chairman.
"I am flattered the Labour Party want to stop me winning this election."