This week will be Barack Obama’s. His anointing in Denver as the Democrats’ presidential challenger will mark the culmination of a campaign that most thought he had little chance of winning in the snows of last winter. To beat the powerful Clinton machine was a formidable achievement. To trap Bill Clinton, one of the consummate politicians of our era, into clumsy campaigning errors on behalf of his wife almost defied belief.

Mr Obama’s choice of running mate, announced yesterday, on the face of it seems sensible. Joe Biden may be known in Britain for plagiarising one of Neil Kinnock’s speeches back in the mists of political time, but to many Americans he will be seen as filling important gaps in the Obama team. At 65 he compensates for Mr Obama’s relative youth and as chairman of the Senate foreign relations committee he makes up for the candidate’s acknowledged lack of experience on the international stage.

The choice of “veep” - vice-presidential candidate - is an important political moment, but what matters most is the candidate himself. Mr Obama’s political appeal is not in doubt, as we will see this week, but his policies are something of a curate’s egg. His prescience on Iraq was impressive, warning that a “dumb war” would immerse America in a long and debilitating conflict and inflame Middle East opinion. But he then blotted his copybook by failing to back a military surge that has worked.

Some of Mr Obama’s other policy positions are also problematical. He has an old-style “tax the rich” instinct which goes against the global trend and which could suppress incentives even in the famously dynamic US economy. An Obama administration would increase the top rate of tax from 36% to 39.5% and also hike capital gains and estate taxes. The American economy, struggling under the weight of the credit crunch and high oil prices, needs this like a hole in the head, even if the aim is to redistribute the gains to lower earners. There is also an instinctive protectionism about Mr Obama, albeit one that he has modified during the campaign, but which remains a source of concern.

Mr Obama will enter the final straight with an acceptance speech on Thursday that is bound to scale new rhetorical heights. His back story is fascinating and so is his potential to be a president who changes America and, perhaps more importantly, how the world views America. Against a conventional “machine” politician he would surely sail to victory, particularly when the Republicans are handicapped by an unpopular president and America’s deep economic woes.

John McCain, however, is no machine politician. His personal history is also fascinating and he, like Mr Obama, emerged as candidate from the position of underdog. As an outsider he, even more than his opponent, has challenged and begun to change his party, notably on issues such as global warming. Mr McCain is a scrapper, who is occasionally guilty of acting first and thinking later, but he brings a breath of fresh air to the contest.

He also brings a lifetime of experience to his candidacy. While his opponent was taking a preconvention break, Mr McCain was swift and firm in his reaction to Russia’s invasion of Georgia. His team were astute in turning Mr Obama’s whistle-stop tour of the Middle East and Europe into a demonstration of his empty celebrity, although less on the ball when it came to fielding questions about the number of homes in the McCain family’s ownership.

There is still much that we do not know about the two candidates, despite all the exposure of recent months. In the next 10 weeks, particularly during their televised debates, we will find out a lot more. It will be a fascinating battle. For once, there really is all to play for.