The differences between David Cameron and Ed Miliband are vast enough to obscure the one thing they have in common. They both went into politics because it seemed like a natural thing to do – a feature that also distinguishes them from most of the population.

Both men are products of rarefied social spheres that made a career in Westminster obvious and available. Cameron, Eton-educated and aristocratically connected, became a Conservative. Miliband’s upbringing at the top table of north London’s Marxist intelligentsia propelled him in the opposite direction. Talent explains their subsequent progress but neither man set off on a path marked by resistance.

For Labour, the comparison is abhorrent. Viewed from the left, there can be no moral equivalence between Cameron exercising the ruling prerogative of his class and Miliband answering the vocation of his secular creed. This righteous indignation has been amplified by Nelson Mandela’s death. For a Labour generation that grew up in the 1980s campaigning against apartheid, today’s veneration of the late ANC leader lends a retrospective moral victory to a decade of political defeat for the left. Margaret Thatcher won all the domestic battles but she was wrong about South Africa. While the Tories were making excuses for white supremacists, Miliband was meeting heroes of the Struggle at his parents’ dinner table.

Cameron was sensitive enough to this blot on the Conservative record to apologise for it in 2006, which confirms that the “modernising” instincts of his early years as leader were sounder than many in his party now suppose. Few voters choose a party for its historic stance on African liberation movements but Cameron understood that support for Mandela had entered British culture as a badge of transcendent values at a time when the Tories were disliked for understanding only material costs.

Now, in abandoning modernisation, he has chosen to concentrate on what seems like good short-term politics – winning the game at Westminster – at the expense of explaining how he thinks politics itself can be good.

That case badly needs making. This week MPs’ tributes to a man who embodied politics as self-sacrifice ran concurrent to a less edifying debate about their own status as salaried professionals. The Independent Parliamentary Standards Authority (Ipsa) thinks an 11 per cent pay rise is in order. Plenty of backbenchers silently agree but their leaders cannot acquiesce at a time when politicians are reviled and everyone else on the public payroll has seen their wages cut or frozen. Cameron has a neat formula for making it clear that MPs are not immune to austerity – “the cost of politics should go down”.

No one wants to be governed by people who are only in it for the money but very few British politicians are. The greater problem is how many of them get into it without experience of doing anything else. In that respect, the differences between Cameron’s and Miliband’s backgrounds are smaller than the career politician label that unites them. Voters might be more receptive to the case for well-paid politics if they thought they were getting a more representative set of recruits for their money. Labour does better than the Tories or Lib Dems on that front but the advantage is slight. Conservatives suffer from their image as a club for the moneyed elite but Miliband’s party is judged to be exclusive in a different way – more a talking shop for do-gooders than a mass movement for working people. The polling agency Britain Thinks recently asked swing voters to imagine a “Mr Labour” figure at a party. They described a shy vegetarian, sorting through the CDs without choosing the music. “Mr Conservative” was brash and arrogant, in an expensive suit, drinking champagne.

Downing Street thinks Mr Conservative has the edge over Mr Labour in one vital aspect – people don’t elect a prime minister to be their friend. The Tories think voters can be swayed by the view that their hard-headed policies rescued the economy and that all gains would be squandered by their weak-willed opponents.

Miliband has scored points with his campaign on the cost of living, playing to Labour’s strength as the party that voters rate higher when asked who better “understands ordinary people”. He still faces doubt, including in his own party, that this empathy is the basis for credible government. The Labour leader’s inner circle has a clear sense of his “One Nation” project as a vision for weaving social justice into the fabric of economic policy. Most Labour MPs are much hazier about what it means in practice. One Milibandite frontbencher estimates that only 10 to 20 per cent of his parliamentary colleagues could easily articulate their leader’s philosophy.

That is a higher proportion than the number of Conservatives who could tell you what Cameron believes. The difference is that the Tory leader seems content to lack vision as long as people think he has a grip. He calculates that voters who despise all politicians will choose a party that shrinks government to fit meagre resources over one that has noble intentions and no way to pay for them.

The Labour leader’s friends say he aims to do much more than tinker at the margins of a dysfunctional economy. He wants to be a great moral reformer but he is running out of time to inspire people with more than just a feeling that he has noticed how expensive life has become.

In an election fought on making numbers add up, Mr Conservative has the advantage of looking like an accountant. Mr Labour’s big heart may not help him much more than his vintage “Free Nelson Mandela” T-shirt. Cameron is comfortable arguing that the cost of politics must come down. Miliband has the harder task of arguing that the value of politics needs to go up.