The policies they espouse are the same. But the philosophies underpinning them are as different as they've ever been. The past week's events in Blackpool have exposed how far apart Tony Blair and Gordon Brown are in their motivations for transforming public services.
For the Chancellor, the private finance initiative is a means of deferring cost and risk in building schools and hospitals. The moral justification is an improved national health service, stronger schools and a fairer society. He derided Tory "privatisation plans" and portrayed the PFI as a means to an end, rather than as a good in itself.
For the Prime Minister, it is more. His moral indignation was directed at a different target, at what he called "the one-size-fits-all, mass-production public service". As he told his audience, a post-Thatcher world of individualised provision is his goal. Bringing private companies into the process is about money and changing cultures. He spoke of a new era of post-comprehensive education, a phrase Brown is reluctant to use. He extolled the virtues of foundation hospitals, independently run, in economic terms that the Chancellor has been very publicly resisting.
Blair told the party (which is not any more the problem) and the unions (which are) that he was embarking on his project regardless of their objections. So did Brown, but not in the same way. He has in recent weeks tried to bring the unions along with him.
Behind the scenes at the conference, there has been a row over tactics. Downing Street and party headquarters were prepared to fight the unions over the PFI. They were quite happy to talk up the prospect of a defeat on the conference floor, paving the way for Blair to cut them down to size in his keynote address.
Both duly happened, the plaudits he received in the media were just what was sought, but the approach has left Brown's supporters uneasy.
When Brown left for Washington on the eve of the conference, for the annual meeting of the IMF, he hoped the argument had been settled. Sure, the government was going to lose a motion calling for an independent review of PFI projects, but this could be offset by a statement from the leadership that all sides could go along with.
The basis for that statement had been worked out a few days earlier by the party's Economic Policy Commission, chaired by Brown. This reaffirmed the government's commitment to PFI in principle, but at the same time spoke of encouraging "a detailed debate beginning immediately".
While Brown was in the US, his advisers spent considerable time on the phone trying to take some of the heat out of the battle, talking to union leaders like Bill Morris and Dave Prentis. The unions had already dropped their call for a moratorium on PFI projects. There would be no backing down on the principle - so what, people around Brown wondered, was the point of fuelling further confrontation?
On his return on Monday morning, however, Brown's people found a statement from the party's ruling national executive committee that was much more belligerent in tone. At the same time, party officials were briefing that any defeat would be ignored. The party was not being consulted on public services, but its concerns on Iraq would be listened to. The logic baffled Brown.
When he delivered his speech, he included several points from the economic commission report that had been brushed aside by the NEC. He promised "to continue to discuss the detailed issues" and said he would ensure that "duty, obligation and service" would remain at the heart of Labour ideals, "and not just markets and self-interest".
Still, the unions had already served notice they would defeat the government in the votes later that day. They expressed their anger further by humiliating Paul Boateng, the chief secretary to the Treasury, by slow-handclapping his speech - and all this as the party is trying with little success to negotiate a new three-year funding deal with the unions.
For the radicals around Blair, spats with the unions are essential to the reform process. They see Labour as just one interest group in a broad church.
Frustrated at being portrayed as a manager first and reformer second, Blair has set his sights not just on cutting waiting-lists and improving standards in schools - mechanistic targets once set are out of the government's hands - but on changing the nature of public services.
Brown is with him, but only up to a point. "The paradox of the modern world is this: we've never been more independent in our needs, and we've never been more individualist in our outlook," Blair said as he began his speech.
The paradox applies to the two men heading the government.