Leading article: Small differences lay bare a big disparity in power

Mr Obama was consistently less keen than Mr Cameron on the need to remove the Libyan leader

In many ways this was a state visit like any other, with the flawless ceremonial and security that customarily attends such events. In atmosphere, though, Barack Obama's stay in London was a world away from the uneasy state visit of George W Bush – the only other US president to accept such an invitation. Darkened by the shadow of an unpopular war, largely hidden from crowds presumed hostile, his was an empty shell of a state visit.

From start to finish, President Obama's sojourn was infinitely more relaxed, spontaneous and simply friendlier – beginning with the early arrival intended to outrun the approach of Icelandic volcanic ash. There was no need for concealment; the Obamas were always going to be an adornment to state and political life, and the Prime Minister was able to bask, albeit briefly, in the President's reflected glory. Warm sunshine made possible such all-American borrowings as a barbecue at No 10 and an open-air press conference at Lancaster House. But there was more than cheerful appearance to the two days. They were as much political summit as state pageant; serious business was spoken and serious signals were sent that were not always indicative of complete harmony.

Of the two political set-pieces, the joint press conference with David Cameron, and the address to MPs and peers in Westminster Hall, the first was the more revealing of the actual state of what Mr Obama – in regrettable deference to British sensitivities – has learnt to call the "special relationship". The second was a rhetorical tour de force that rose to the splendour of the surroundings and yielded little to the President's Cairo speech in its sweep and significance as an expression of his international credo.

Whether it was intended as such or not, the President's decision to give such a definitive and substantial speech in London can be seen as a compliment. It was as eloquent and confident a defence of universal rights, freedoms and aspirations as has been heard here for a long time, while refreshingly free of dogma. His praise for the "patchwork heritage" that had made it possible for "sons and daughters of the colonies" to sit in Parliament, and for "the grandson of a Kenyan who served as a cook in the British Army to stand before you as President of the United States" was the one line that brought spontaneous applause – and not a few damp eyes.

Back in the all-too-real present, however, there are clearly differences between London and Washington that the Prime Minister and the President did their best to steer around in their public statements. One concerns the recipes chosen by the two governments for economic recovery. Mr Obama carefully granted that the choices made would be "difficult", but also "different".

A second relates to Afghanistan. Mr Cameron, along with much of Britain, is impatient for troops to be withdrawn now that Osama bin Laden is dead. Mr Obama spoke of starting the transition to Afghan sovereignty, with military withdrawal to begin late in 2014. Will the British government be prepared to stay that particular course?

The greatest differences remain, ominously, on the most pressing issue: Libya. While mounting a forthright defence of the intervention, Mr Obama was consistently less keen than Mr Cameron on the need to remove the Libyan leader from power and even from the country. He stressed that the US had no hidden arsenal that it could – or would? – use to resolve the conflict, and stuck to the UN-mandated "protection of civilians". Despite what we must now apparently call the "essential" relationship, the message from Washington, delivered by the President in person, is that Britain would do well to follow Mr Obama's preference for realism over idealism, and tailor its ambitions to its capabilities.