For the first time in Labour's history, party members will return leadership ballots, which hit their doormats yesterday, without knowing who will win. That is because Ed Miliband rejected a Bobby Kennedy role, seeking to influence his brother's leadership from a kitchen-table seat. A significant political disagreement with his brother gave him reason to believe that his advice would seldom be taken.

That argument has finally moved to centre-stage as the campaign closes. It is not about different world-views -- both are social democrats who believe that Labour's mission is to narrow the gap in life chances, albeit with mildly different instincts about how to get there. And the brothers have resisted excessively personalising their fraternal battle, to the mutual frustration of some supporters.

What the Milibands really disagree about is why Labour lost and how to win again. Couching the argument in psephological number-crunching about the shifting class structure, they are playing out a deeper existential question about the party's strategy and public identity. What does "moving on" from New Labour mean, and how deep should it go? David Miliband warns that throwing out too much of a recently successful formula could mean a long spell in opposition; Ed Miliband fears that it is failing to recognise the scale of change needed which would keep the party from power.

David Miliband's campaign presents the election as a "head versus heart" choice. The idea that Ed Miliband is a "comfort zone" candidate irks John Denham, the Southampton MP who has focused most on Labour's southern challenge and who is leading on future policy development for Ed Miliband's campaign.

Denham warns that what he calls the "New Labour establishment" could fatally underestimate how much must change. "It is Ed Miliband who is the brave choice, who says 'we are going to have to change again as we changed before' against those who think we have still pretty much got it right and need to tweak things a bit to return to our winning formula," he says.

The sharpest argument in the party's inquest into May 2010 is not about this May but Labour's last victory five years earlier. Whether to treat that as a triumph or near-disaster could determine whether "change" is in a major or minor key. For Liam Byrne, the main election number cruncher backing David Miliband, the "simple fact" about 2005 is that "Labour won", with the historic 1997 New Labour coalition "sustained to carry Labour to victory once again". Byrne's Progress paper on the 2010 defeat argues that the lessons of 2005 were "much misunderstood", alluding to fierce internal arguments over the analysis he produced at Tony Blair's behest that autumn, just as New Labour factionalism hit new lows.

Contrast 2005 with 2010 and the message is "carry on New Labour". The recession, Gordon Brown's brooding presence and the MPs' expenses crisis all deepened a "time for a change" mood after 13 years in power. These one-off factors shall pass. Even in soberly assessing Labour's 29 per cent share, Byrne declares "our coalition was cracked but not broken".

Denham is unconvinced. A focus on the one million votes lost after 2005 "misses the point" of the four million votes lost before 2005. Thirty-five per cent could just be enough under first-past-the-post, if votes fall happily, but how often should Labour expect as unattractive an opponent as Michael Howard? In this view, Humpty-Dumpty cannot be put together again: the deep fracturing of New Labour's electoral coalition demands a more fundamental reappraisal.

New Labour already had a "one more heave" victory in 2005 and surely experienced a "one more heave" defeat in 2010. Gordon Brown ran on "change" yet failed to define it. Why? Ultimately, because he could see no viable alternative to the New Labour election playbook.

"We quickly defaulted to a textbook New Labour campaign," says Patrick Diamond, who worked at No 10 for both Blair and Brown. "Brown never took the chance to recast New Labour: was it that the opportunity didn't really exist, or was it a failure of imagination or courage?"

Diamond, who has not endorsed a leadership candidate, believes that the next leader must realise that a strategy of "consolidating New Labour modernisation" will fail. "It simply leaves too many questions unanswered" about a very different world, he says, and underestimates the coalition, too.

Core votes?

Premature obituaries for Labour now date back a half-century to the Must Labour Lose? Penguin special of 1960. New Labour escaped death by sociological treatise, yet now finds a sting in the tail. A party on 29 per cent is assumed to have "retreated" to its "core vote". Yes, even as Labour's vote fell across 2001, 2005 and 2010, each election produced the most balanced cross-class pattern of votes in the party's history. New Labour's professional support proved much more resilient than the so-called core vote, which collapsed.

"The core Labour vote that some thought could be taken for granted became the swing vote that went Conservative," wrote Ed Miliband in his recent Fabian essay. The dramatic post-1997 slump in DE share alone cost Labour 40 marginal seats in 2010: the difference between opposition and government.

But the former Scottish secretary Jim Murphy, co-chair of the David Miliband campaign, tells me: "A core vote strategy guarantees you opposition. It fails the Downing Street test. The road back to power isn't inverting the mistake of New Labour and describing that as a strategy." Yet the pejorative expression "core votes" is misapplied to those voters most likely to switch.

"It is dangerous to pretend that we don't need the middle classes," warns David Miliband. His brother could hardly disagree, but he does argue that New Labour has also understood the loss of middle-class support -- too often dismissing liberal critics as a noisy, unrepresentative Guardianista niche, though AB and C1 voters have been twice as likely to go yellow as blue. Labour's working-class and middle-class challenges mirror each other, in the scale of substantive policy change and symbolism required on both economics and social liberalism to reconnect.

This argument between the Milibands is often narrower than that between their supporters. David Miliband would represent more continuity than his brother, but knows that the next leader must credibly substantiate the claim to "change". His argument that "an alphabet analysis can lead you backwards into the triangulation politics which led to our downfall" signals his own critique of New Labour.

If the coalition lasts until 2015, the next election -- coming 18 years after 1997 -- would take place in a Britain as distant from Tony Blair's first victory as that landslide was from Maggie Thatcher's defeat of Jim Callaghan. The new leader might find inspiration in the history of how Labour built a broad winning coalition in 1997, 1966 or 1945. But they will have to build Labour's next governing majority for themselves.

Sunder Katwala is general secretary of the Fabian Society [2].