Mr Cameron said Tories would take a "brazenly elitist" approach to the school system, barring anyone without a 2.2 degree or better from teaching and giving heads the power to sack failing teachers and reward high-performers with bonuses.
Meanwhile Mr Brown promised a new National Internship Service to give 10,000 undergraduates from poorer backgrounds greater access to professions like medicine and the law.
The theme of aspiration is likely to be a key battleground in the campaign for the election which must be held by June 3 but is widely tipped to be called for May 6.
Mr Brown signalled his determination to woo the vital middle-class vote in a speech at the weekend in which he promised to unleash "the biggest wave of social mobility since the Second World War".
Business Secretary Lord Mandelson tonight said today's package indicated Labour was fighting on "a programme based not on core votes but on our core values of raising aspiration, expanding life chances and building a Britain of opportunity for the many, not the few".
As well as the National Internship Scheme, Mr Brown and business minister Pat McFadden unveiled plans for structured assistance for the 130,000 brightest secondary school pupils from poorer backgrounds; a new Social Mobility Commission to produce an annual report on moves towards a fairer society; and a Gateways to the Professions Forum involving representatives of 60 key professions.
The initiatives came in response to last year's report on access to the professions by Blairite former Cabinet minister Alan Milburn, who today said he was pleased the Government had put "social mobility at the heart of its agenda".
Meanwhile, Mr Cameron identified improved teaching standards as the key to improving the chances of Britain's young people.
Launching the Tories' draft education manifesto in south London, he set out plans to attract the brightest graduates into teaching, with an offer to pay off student loans and provide bonuses for those who perform best in the classroom.
He also announced plans for a Teach Now programme to allow people to transfer from professions such as banking and the law into teaching without having to do more exams, saying "only the best professionals with the best qualifications need apply".
"We're committed to a comprehensive programme of reform to elevate the status of teaching in our country," said the Tory leader.
"We want to make it the noble profession - the career path that attracts the best brains, is well-rewarded and commands the most respect."
His plans were dismissed as an "airbrushed re-announcement" by Schools Secretary Ed Balls, who claimed that Conservative spending plans would mean fewer teachers and larger class sizes.
And they gained a lukewarm response from teaching unions, with NASUWT general secretary Chris Keates accusing him of undermining morale by "denigrating and casting doubt on the quality of teachers currently in service".
Mary Bousted, general secretary of the Association of Teachers and Lecturers, branded Mr Cameron's plans "redundant" at a time when Ofsted has rated the UK's teachers the highest-qualified ever.
"If school budgets are not increased then it would only be possible to pay some teachers more if pay is cut for others," added Dr Bousted. "This would do little to solve recruitment and retention problems."
Shadow Universities Secretary David Willetts said that social mobility had "stagnated" under the Labour Government and accused ministers of focusing on the symptoms rather than the cause.
"Young people need more good schools and more good advice, which are the two key issues which the Government has ducked," said Mr Willetts.
"Young people don't lack aspiration. They lack guidance through the maze of qualifications which the Government has created. That is why Alan Milburn was right to recommend the creation of an Independent Careers Service. But the Government has yet again rejected the idea despite it being one of the most important in the whole report."
But Mr Brown said: "We can't be a truly aspirational society if some people are still denied the chance to get on, and although we have raised the glass ceiling, we have yet to break it.
"That is why our priority will be to remove all the barriers that are holding people back."
Mr Milburn said the Government should get rid of "any vestiges of a closed shop mentality" in the professions and ensure they are open to talent from all parts of society.
"The chances of social mobility are greater if more people get the chance of a professional career," said the former Health Secretary.
"At present the default setting in too many professions, particularly at the top, is to recruit from too narrow a part of the social spectrum.
"It is not just that such elitism is unjust socially. It can no longer work economically. The UK's future relies on using all of our country's talent not just some of it."
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