Supporters and opponents of independence argued over the best way to protect the NHS during the BBC's Big, Big Debate in Glasgow.
Scottish Green Party MSP Patrick Harvie claimed independence was needed to protect against a "nasty, competitive, profit-driven motive" towards the NHS.
But Respect MP George Galloway argued there would not be an NHS without "a country big enough" to share resources.
The politicians debated in front of an audience of nearly 8,000 young people.
The audience of 16 and 17-year-old first-time voters at Glasgow's SSE Hydro arena was drawn from secondary schools across Scotland.
The NHS has become a key battleground in the referendum debate, with supporters of a "Yes" vote claiming independence was needed to protect it from a "privatisation agenda" being pursued by the UK government for the NHS in England and from budget cuts.
However, supporters of a "No" vote have argued that NHS policy is already devolved to the Scottish Parliament, and have questioned whether an independent Scotland could afford to maintain spending on healthcare.
BBC research has found that the debate about the economy, currency, welfare and pensions are important to them as they ponder how they will vote in next week's referendum.
More than 1,000 16 and 17-year-olds filled in a questionnaire ahead of the BBC's SSE Hydro debate.
Mr Harvie, representing Yes Scotland, said: "There's a difference between being able to control policy on something like the NHS and being able to control Scotland's finances.
"Now, right now the UK government is dead set on breaking up and privatising the structure itself of the NHS.
He added: "If that leads in the longer term to more introduction of fees and charges, if it leads to a decline in the public resources that are going in, that will impact on the Scottish budget."
What the young audience said
What the young audience tweeted
He attacked what he saw as a "nasty, competitive, profit-driven motive" and argued Scotland needed "control of its own finances and its own voice at a European level".
Mr Galloway, representing Better Together, said: "We would never have had a National Health Service if it wasn't for two things: a Labour government in 1945 and a country big enough to make a big enough pot to share resources across the country in order to have healthcare free at the point of need.
"The National Health Service is an entirely devolved matter. It could only be privatised if people were foolish enough to elect a Scottish government that was ready to privatise it."
The Respect MP for Bradford West added: "The Tories will be out in the spring. The privatisation agenda will be dead in the spring."
A former Glasgow Labour MP, Mr Galloway was expelled from the party in 2003, but claimed he was speaking for "real Labour values" in the debate.
The SNP's Nicola Sturgeon, representing Yes Scotland, asked: "How many times has Scotland voted Labour to end up with the Tories? Why do we have to cross our fingers and vote for a Labour government when we can vote 'Yes' and guarantee we always get the governments we vote for?"
The former health secretary added: "I know how hard it is to protect the budget of the health service when our overall budget is being reduced by Westminster.
"I will fight with every breath in my body to keep the National Health Service in public hands, but we are going to be more able to do that when we are in control of our own budget so that we set our own priorities."
The debate took place on the day that think tank the Institute for Fiscal Studies said an independent Scotland would need to borrow more or tax more to increase spending on the heath service.
Scottish Conservative leader Ruth Davidson, representing Better Together, said Ms Sturgeon had "not answered the quote from the Institute of Fiscal Studies, who run the numbers, who said that health spending and health consequentials that got sent up to Scotland weren't spent on health.
"The Scottish government has chosen to protect the NHS in Scotland less than it has been protected in England."
The IFS, which has not taken a position on independence, said that, until 2015/16, Scotland would not have to cut public spending to the same degree as the rest of the UK if it stays in the Union.
This is because Scotland receives more through the Barnett formula, which determines the distribution of public spending around the UK.
The panel at the Hydro faced questions from the audience, who were divided between supporters of "Yes" and "No", with some undecided voters also attending.
The referendum on 18 September will be the first time 16 and 17-year-olds have been given the vote in Scotland. The minimum voting age for elections is 18.