Barack Obama's groundbreaking victory marks a giant step for politics but just a small step for transatlantic relations.
His political achievement is being widely welcomed and acclaimed across Europe, but no one expects significant changes in EU-US ties.
Conservative MEP Jonathan Evans said: "Despite the fact that this is an historic moment, despite all the expectations, particularly arising from a Barack Obama victory, some people might be disappointed to find that not very much in terms of actual policy (towards Europe) will be different.
"There may be a difference of engagement with the EU but we would be very foolish if we assumed that Barack Obama will represent a completely new approach."
Mr Evans, a member of the European Parliament's delegation for relations with the US Congress, went on: "Having said that, a new president does present a huge new opportunity, because although George Bush had become more engaged with Europe during his second term of office, he did not entirely overcome the damage in relations caused by the Iraq war."
From Europe's point of view, some EU-US policies would change for the better under either Mr Obama or Mr McCain. Others would be advanced more by Mr Obama - and others more under a McCain administration.
Mr Obama will certainly change America's stance towards climate change - but so would Republican Mr McCain.
And while Mr McCain's free-trade stance would have been welcomed in Europe to help revive stalled world trade talks, President-elect Mr Obama's protectionist tendencies make him potentially tougher to deal with, not just on trade but in tackling the global economic crisis.
On defence, Europe would have been under renewed pressure from Washington to step up military spending in the Nato alliance whichever man won the White House.
And on foreign policy, a less hawkish Democrat in charge might be welcome in terms of scaling back the US presence in Iraq, but Mr Obama has already made clear he wants a significant military commitment from the UK and other European allies in Afghanistan.
"That pressure may be harder to resist if Europe can no longer complain about Bush-style unilateralism in foreign policy," said Mr Evans.
"President-elect Obama could turn out to be carrying a fist in a velvet glove and he will challenge very hard on defence spending, just as McCain would have done."
In the European Commission, officials agree that the extraordinary political symbolism of Mr Obama as president is not matched by the humdrum day-to-day political reality of transatlantic relations.
One senior insider said: "The fact is that, despite the political fallout in Europe from the Iraq war, we have been getting on well with President Bush in about 98% of policy matters.
"French President (Nicolas) Sarkozy loves America, which has helped largely to overcome the post 9/11 problems. Germany's Chancellor Angela Merkel is broadly in tune with US thinking despite having an anti-American foreign minister and the UK relationship is, of course, well-established.
"On policy, the US is dependent on oil, so shares EU energy concerns, and there will now be more in common on climate change.
"The key stumbling block will be a world trade deal, as well as details of US security and foreign policy, where we see Obama as more accommodating on Middle East policy than McCain."
Socialist leader in the European Parliament Martin Schulz said he hoped the president-elect would act to put a reform programme in place to renew EU-US links.
He said: "It is time for a new dawn in relations between our two continents. We need more than ever to work together to tackle problems such as economic recession and the creation of a new world financial order.
"President Bush squandered US potential to contribute to global progress by his divisive, unilateral approach to issues such as security. The new president should make an immediate symbolic gesture by announcing the closure of the Guantanamo Bay detention centre and the abandonment of the missile installations planned in Poland and the Czech Republic.
"The tension and division caused by the Bush regime's policy on such important global issues as international stability and climate change must be relegated to the past.
"I appeal to the new president to make sure that Europe is on the top of his in-tray. We must start working together from day one - and together we will find the solutions the world now urgently needs."
European Commission president Jose Manuel Barroso addressed a plea to the new US president in September.
In a speech at Harvard, he explained that he was able to do so because, whoever won the White House, Europe's message would be the same, and so would the issues confronting the EU-US relationship.
Mr Barroso declared: "In these times of uncertainty, the EU needs the US and - yes - the US needs the EU more than ever."
It is a message EU leaders hope President-elect Obama will endorse.