Recounting a conversation with a friend, a white woman said that, after so many decades of the struggle for women's rights, it was disheartening and unfair that Hillary Clinton's historic candidacy was in danger of being derailed by that of the first-term junior senator from Illinois.

As she spoke, I saw her neighbour, a retired black professor, staring grimly at his plate. Face averted from her, still looking down, he said: "Anyone - anyone - who equates the situation of women in this country with the struggle for civil rights by blacks is talking bullshit." That was an utterly unexpected word from him - a man of graceful and formal manners - and the shock of it reverberated down the table.

I wondered how many leftish-leaning dinner parties across America were at that moment fracturing, like this one, along the lines of race and gender, not to mention the lesser ones of age and class. From the angry and affronted talk of their supporters, it would be hard to gauge that the policy differences between Obama and Clinton amount to no more than slight nuances and shades of emphasis (should we penalise people for failing to buy subsidised health insurance? Clinton says yes, Obama no - and that's about it, so far as rival ideologies are concerned).

Yet the battles now raging between otherwise like-minded Democrats, in this most passionate American election in living memory, are being fought in bloodbath terms. When Ted Kennedy endorsed Obama, the president of the New York chapter of the National Organisation of Women issued a press release saying, "Women have just experienced the ultimate betrayal," and Obama supporters are hardly more temperate as they zealously sift through every utterance by Clinton and her surrogates in search of encoded racism.

Obama has done himself no good with his occasional forays into sexism, like his fraternity-jock remark at the New Hampshire debate, delivered with a cocky smirk, "You're likeable enough, Hillary," or his observation at Tulane that, "You challenge the status quo, and suddenly the claws come out". A phrase has entered the language around Clinton's candidacy: "vagina voting".

No wonder, then, that the results on Super Tuesday confirmed the theme of earlier primaries - people casting their vote not on the issues of the day but on the basis of their sex, age, income group and skin colour. Blacks broke for Obama by four to one, Hispanics for Clinton by nearly three to one, which won her the states of California and Arizona, and will probably win Texas for her on 4 March. Clinton carried the so-called "beer Democrats" earning less than $50,000 a year, Obama the "wine Democrats" earning more than $100,000. She got the old, he the young.

So clear was this pattern that, a couple of days after Super Tuesday, a memo from within the Obama campaign was either leaked or accidentally escaped, which forecast that he was set to lose Maine, Texas, Ohio, Pennsylvania, Rhode Island, West Virginia and Kentucky, for reasons obvious to anyone following the election: too many Hispanics, too many old people, too few college students, too many middle-aged white women, too few blacks, or too many working-class voters. The memo was a dispiriting exercise in demographic fatalism - especially considering Obama's enormous majorities in the caucuses of Washington state and Nebraska on Saturday, where he cut deep into Clinton's presumed constituencies.

What's being missed here is that, although their policies are so similar as to be nearly identical, an Obama administration would be entirely different in character from a Clinton one. A presidential administration is, after all, the third executive branch of government, alongside the judiciary and the legislature, and consists of a cast of several thousands - advisers, aides, appointees, along with their separate staffs. The president may fulfil any one of a multitude of roles within his or her administration, from ghost-written poster child to relentless micromanager. More important than Obama's ever-lengthening baritone aria, "To Heal a Nation and Repair the World", now running at 50 minutes-plus, and which repetition is fast turning into white noise, are his more prosaic statements about what kind of an administration he would bring to Washington, and how he would function in relation to it.

"I think I'm very good at teasing out what the issues are from people who are smarter than me, and synthesising their arguments," he said in an interview with the Reno Gazette-Journal. His senior economic adviser, Austan Goolsbee, confirms that. "He likes to bring in three or four people who disagree with each other. Then he'll have them debate while he quizzes them." During a spat with Clinton in Las Vegas, Obama said, "I want to gather up talent from everywhere."

Such promises are as important as any he's made along the campaign trail, and they're perfectly consistent with his style in interviews and town meetings, where he listens closely, cedes one point, demurs on another, and hesitantly articulates a position that was never in his scripted talking-points. In Obama one sees - as one never sees in Clinton - a catholic, open-minded intellect working in real time, and he seems admirably unashamed of his own uncertainty.

When he says, "I think...", as he often does, you know he's really thinking. As a memoirist, he showed a remarkable capacity to comprehend imaginatively the lives of other people, in Africa and Indonesia as in the US, and you can see that gift at work in his exchanges with questioners. Obama offers the prospect of a first-among-equals administration, more flexible, more empiricist, more imaginative and less ideologically driven than any in recent history.

By contrast, remember how Clinton micromanaged her first healthcare plan to death in 1993, brooking no argument and taking no prisoners. Her superb grasp of policy details goes, unfortunately, hand in hand with a siege-mentality defensive centrism. Unlike Obama, she is certain to a fault. Where Obama wings it, she goes by the script.

When she made her concession speech in Des Moines after the Iowa caucuses, she was flanked by Bill Clinton and Madeleine Albright: a grimly prophetic tableau, I thought, heralding a return to the orthodoxy of the Democratic Leadership Council ("the Republican wing of the Democratic party", as Howard Dean once called it), circa 1990 and to the poll-based politics of triangulation.

Two presidencies are in competition here: one driven from the bottom up, by a former community organiser; the other from the top down, by a combat-toughened former corporate lawyer. There are fundamental structural differences between the two campaigns and the two prospective administrations, but instead of focusing on them as we should, we're still fighting over dinner tables because one of the candidates is a white female and the other a black male.

Jonathan Raban's books include 'My Holy War: Dispatches from the Home Front', a collection of post-9/11 essays published by Picador