The Conservatives say they will expand the number of academies in England to create at least 220,000 "good school places" over the next nine years.
The plans focus on almost 32,000 children in deprived areas, who appealed unsuccessfully against the secondary schools they were allocated.
The expansion of Labour's policy would involve scrapping the ban on creating schools where there are spare places.
Tory leader David Cameron said the plans would "drive up standards".
Under the proposals, the party says capital funding would be provided and planning rules loosened to allow groups such as charities and concerned parents to set up schools more easily.
A Conservative education "green paper" published on Tuesday proposes reallocating 15% of the money in the government's Building Schools for the Future refurbishment programme.
The party says this would release £4.5bn for the new academies.
NUT leader Steve Sinnott said it would "impose a massive cut on funding for already promised new schools and school repairs".
But the Tories said funds that had been committed already would be protected. They believe the new "good" schools would attract pupils - and the funding that goes with them - from existing schools.
Mr Cameron told BBC One's Breakfast: "I think the way we will really drive up standards is to bring new schools into the system to improve creativity...
"I don't believe that a new good school coming on stream somehow damages all the other schools."
The Tories are adopting the idea of a "pupil premium" for children from the most disadvantaged backgrounds.
Although schools get extra money if they are in areas of deprivation, this does not focus on individual children in need, they say.
Shadow children's secretary Michael Gove said: "The simple fact is there are not enough good school places, especially in the most deprived parts of the country.
"As a result, we are condemning many children to a life of underachievement and deprivation or long journeys to schools miles away from their home."
But Schools Minister Lord Adonis said: "People will ask why we need a new academies programme when the current academies programme is working well, is popular with parents, is driving up standards in disadvantaged communities and is now being accelerated so that we will have 230 academies by 2010 and more to come."
He added that government investment was already recruiting thousands of teachers and would see 400 new secondary schools built by 2011.
Lord Adonis said: "The key difference between us is that they think this process can take place without local authorities.
"If that's the case there will be fewer good schools because we need local authorities to provide the sites."
There were also questions over paying for the Conservative scheme, he added.
Liberal Democrat schools spokesman David Laws said: "These new Tory policies fail on two key tests: funding and selection.
"David Cameron is effectively giving the green light to more grammar schools in areas such as Buckinghamshire.
"While the Tories talk about targeting extra funding on the most disadvantaged pupils, it seems that no new money is actually involved."
Chris Keates of the NASUWT teachers' union said the Tory plan would create social segregation and chaos.
"State education is a public service which should be democratically accountable at local and national level not handed over to anyone who has a passing interest in education," she said.
"Parents who want to be more actively involved, can do so by engaging in their own children's education, joining parents groups and serving on the governing body."
The head of the Association of School and College Leaders, John Dunford, said: John Dunford said: "The number of admissions appeals cases by parents does not indicate that there are too few good state schools places.
"It means that parents have been given false expectations of their ability to choose any school they want for their children.
"Parents already have the power to set up schools but in actual fact very few have taken it up."