The Tories claim 94% of working households are better off under the tax and benefit changes coming into effect.
Labour's Ed Balls claimed average families were £1,100 a year worse off since 2010, including Monday's changes.
Both parties say their rivals have secret plans to raise taxes if they win the general election.
The Lib Dems, meanwhile, are angry with the Conservatives for claiming credit for an increase in the personal income tax allowance, which they say they had to force Tory ministers to accept.
The personal allowance - the amount someone can earn before they are taxed - has gone up from £10,000 to £10,600.
The Tories and Lib Dems have both said they want it to go up to £12,500 by 2020, but senior Lib Dem David Laws said his party would implement this "far faster".
In other news:
Shadow Chancellor Ed Balls, speaking in Leeds, said Britain could not afford five more years of the Tories.
"Families are £1,100 a year worse off on average - that is the true cost of a Tory chancellor," he said, citing independent figures from the Institute for Fiscal Studies which he said supported his case.
He said the IFS figures took into account all of the changes David Cameron and his government had introduced since May 2010 up until Monday, including the change to the personal allowance. The IFS "also exposes how families with children have been hit hardest", he added.
"Their damning conclusion is that low-income households with children lose the most as a percentage of their income from changes implemented by the coalition.
"While millions are paying more, we know that millionaires are paying less."
He repeated Labour's claim that a Conservative government would increase VAT to make their sums add up - something denied last month by David Cameron.
The Conservatives claim Labour would be forced to increase National Insurance contributions to pay for their spending plans.
By Carole Walker, BBC Conservative Campaign Correspondent
David Cameron and George Osborne will both be out campaigning in the South West on the day tax changes affecting millions of voters take effect.
Mr Cameron will be meeting some carefully selected voters who will benefit from the changes. The opposing parties are already hurling conflicting statistics over how many of us have gained or lost under the outgoing government.
The apparent contradictions reflect the fact that the opposing parties are choosing different figures. So Mr Cameron will point out that more than 90% of working households will be better off under the changes which come in today, largely due to the rise in the amount we can earn before we pay tax.
Labour has countered that families are on average £1,100 a year worse off because of the tax and welfare changes since 2010; much of this is due to benefit cuts.
David Cameron will say there is not just an economic case but a moral case for low taxes, saying this goes to the heart of what he believes in as a Conservative.
But in an apparent acknowledgement that many people do not yet feel they are benefitting from the upturn in the economy, he will say: "I don't just want people to see Britain's recovery on the TV or hear it on the radio, I want them to feel it in their lives."
He'll claim that today's changes will help that to happen.
Few of us want to hand over more of our earnings in taxes, but as we saw in last week's television debate, some of his political rivals are mounting strong arguments that taxes should be raised for higher earners.
There is another flipside to the commitment to low taxes.  The Tories need to save £30bn to eliminate the deficit by 2017/18 and if they won't put up taxes, all the money will have to come from spending cuts.
They have said they will save £5bn by cracking down on tax avoidance, £13bn from departmental spending and £12bn from welfare. But there remain big unanswered questions on which benefits and which government projects will have to be axed.
Liberal Democrat leader Nick Clegg blasted Labour's policies as "economically illiterate", but also warned that Chancellor George Osborne was "a very dangerous man" because of his plan to balance the books by spending cuts alone.
One of the biggest changes coming into force on Monday is the relaxation of pension rules, so that those with a defined contribution pension "pot" can take out as much as they like when they reach the age of 55.
Liberal Democrat Pensions Minister Steve Webb said the principle was to trust people with their own money - but he urged people to seek advice and not rush into any decisions.
This election issue includes income tax and national insurance levies and business taxes.
Labour's pensions spokesman Gregg McClymont welcomed the "flexibility" in the new system but voiced concerns the pensions industry was "finding it difficult to adapt so quickly to such a big change".
Other changes coming into effect include a higher limit on ISA savings, the Marriage Tax Allowance, a 2.5% increase in the state pension, the abolition of employer National Insurance on under 21-year-olds and the scrapping of the 10p tax band on savings. Working age benefit increases have also been capped at 1%.
The Conservatives have produced Treasury figures suggesting 94% of households will be better off under the changes, with 92% of pensioner households also gaining. The figures do not include workless households.
In his speech, Prime Minister David Cameron will say: "Today is a big day for our country. It's 'money-back Monday' - a day when, quite simply, hardworking taxpayers get to keep more of their own cash."
He will add that as a result of Conservative action - including raising the personal allowance - "our country becomes a better and fairer place to live… where those who put in, get out; where hard work is rewarded; and people are trusted."
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The official start of the new tax year has sparked a fresh battle between Labour and the Conservatives over their respective economic plans.