Hell hath no fury like leftish politicians scrapping over social policy. On the surface, the ideological divide between the two leading women in Scottish politics, SNP deputy first minister Nicola Sturgeon (pictured, on left) and Scottish Labour leader Johann Lamont (right with Scottish TV presenter Rona Dougal), appears wafer-thin. Both treasure Scotland's NHS, free of internal markets and rapid commercialisation. They have trumpeted the country's system of free personal care for the elderly. But, with costs rising by 160% in less than a decade, Lamont has questioned whether the country can afford wholesale universal provision.

When the two women clashed recently in a Scottish TV debate, the nub of the SNP-Labour divide came down to the lower-key Lamont's realism versus the idealism-cum-populism of Sturgeon, who wants to harness billions for a Nordic-style social state.

One exchange was revealing. Sturgeon urged Scots to vote yes on 18 September to ensure that the country could "take control of economic and social policy to create a fairer Scotland". Lamont retorted: "It's not enough to say fabulous things. We have to know how those ... will be paid for."

And, in an English context, some fabulous things are promised in the SNP government's 650-page independence white paper, Scotland's Future, overseen by a combative Sturgeon. In the document this Nordic model is lauded. It rightly portrays welfare policy as a social investment, rather than a drag on the state.

Prominence is given to a universal system of high-quality childcare from the age of one "to match the best in Europe". It is acknowledged that this will need massive investment, with an estimate of 35,000 new jobs. If Denmark can do it, why not Scotland?

Yes, an independent Scotland could reach those Nordic social heights with a tax rate to match, and an end to the seven-year council tax freeze, which Scottish Labour says has led to the rich prospering and 35,000 council job losses, with those who most need the help of local authorities losing out.

The SNP government has refused to use its limited revenue-raising powers to vary income tax by up to 3p, preferring to rely solely on an annual Westminster block grant of around £30bn. Even levying 1p extra might raise about £350m annually – enough to begin addressing pressing social issues such as an appalling health record: life expectancy (the white paper admits) is "lower than in all other western European countries".

At least one leading Scots economist says this grant has kept the Scottish government in a comfort zone, avoiding tough decisions while keeping the middle classes happy with no extra taxes.

The SNP government says: "There will be no requirement for an independent Scotland to raise the general rate of taxation to fund existing levels of spending." But what about funding, say, that ambitious childcare programme, or the pledge for a welfare system that ensures benefits and tax credits rise at least in line with inflation?

Much of England thinks a yes will set Scotland apart. In fact, for 15 years, the country – already with its own institutions, from NHS Scotland to an independent judiciary and legal system – has steered a social democratic course at odds with both New Labour and the coalition. All of which has pushed the Scottish Tories, led by Ruth Davidson, further to the sidelines, with the Liberal Democrats also marginalised.

The coalition's rightward drift towards a small state may be fuelling the yes campaign in working-class areas. In the 22 most deprived neighbourhoods, 47% of respondents in Ipsos Mori Scotland polls say they will vote for independence. In the 22 most affluent areas, only 26% plan to do so.

The SNP government is spending £20m to reduce the impact of the bedroom tax, plus a £33m welfare fund to help those who have hit rock-bottom. Soon an expert working group will report on the provision of broader welfare, after independence. The big question is how this is to be funded – will it be answered before 18 September?