They did Tuesday at Bill Clinton's annual international aid conference.
It was a rare opportunity to compare and contrast, a clash in New York of the White House incumbent and the challenger.
Obama is still the bigger draw, with long lines forming 90 minutes before to hear him. Romney did not come close to matching that, although this might have been in part because he was speaking early in the morning, just after 9am, with people still making their way from breakfast.
Romney, under huge strain after a series of campaign disasters and polls showing him trailing Obama, rose to the occasion. Normally a poor speaker, often dismissed as 'wooden', he was surprisingly poised and relaxed and his delivery relatively smooth. He also dispensed with his normal stump speech and largely avoided attacks on Obama, instead making a case for tying international aid to free trade deals and stimulating the private sector.
By contrast, Obama looked tired, as if he is the one that should be under strain in the election race rather than Romney. But, even tired, Obama is a better speaker than Romney.
He devoted his speech to human trafficking, an emotional plea to tackle what he described as "barbaric" problem, modern-day slavery. He sounded as if he was addressing a much bigger theme than Romney's, and with passion.
Both were speaking at the Clinton Global Initiative conference, the aid foundation set up by the former president which delivers millions of dollars to the developing world each year. Those attending are a mixture of leaders from the developing world, philanthropists, corporate representatives and the heads of non-governmental organisations.
The conference audience leans more towards Obama than Romney. Romney received a standing ovation at the start of his speech. Obama received one at the beginning and end.
On the face of it, the conference was potentially awkward for Romney, given that it is being hosted by Clinton, who delivered a widely admired speech of the Democratic convention in which he made the case against a Romney presidency. That speech helped contribute to Obama's campaign bounce.
But Clinton, introducing Romney, was cordial and Romney smiled as the two stood at the podium. The two shook hands and Romney was on.
It was not only that Romney's delivery has improved, he also managed to laugh at himself.
"I appreciate the kind words and your invitation here today. If there's one thing we've learned this election season, it's that a few words from Bill Clinton can do any man a lot of good … After that introduction, I guess all I have to do is wait a day or two for the bounce."
The core of Romney's speech was international aid, promising that as president he would tie it to encouraging the private sector in the developing world and to free trade deals, what he called a Prosperity Pact.
"For American foreign aid to become more effective, it must embrace the power of partnerships, access the transformative nature of free enterprise, and leverage the abundant resources that can come from the private sector," he said.
The closest he came to criticising Obama was saying that Americans were "troubled" by events in the Middle East. He also, without naming him, described the Iranian leader Mahmoud Ahmadinejad, attending the UN general assembly, as "a voice of unspeakable evil and hatred".
When Obama arrived, Clinton went one better than a handshake, giving the president a hug. Obama, returning the favour, praised not only Clinton's speech to the Democratic convention but Hillary Clinton for her grace and grit that he said had made her one of the finest ever secretaries of state, a tribute that helps in building her up for a potential 2016 presidential run.
Obama, who has opted for more sober, downbeat speeches this year, offered glimpses of the speaker he had been in 2008, making an emotional plea for an end to worldwide human trafficking. He put it in the context of the Emancipation Proclamation, a copy of which was hanging from the wall of his office in the White House.
Human trafficking, Obama said, "ought to concern every person, because it's a debasement of our common humanity. It ought to concern every community, because it tears at the social fabric. It ought to concern every business, because it distorts markets. It ought to concern every nation, because it endangers public health and fuels violence and organised crime. I'm talking about the injustice, the outrage, of human trafficking, which must be called by its true name – modern slavery."
He promised the US would tackle the problem more vigorously than it was at present and announced a few measures. In reality, though, the US does little, as Clinton acknowledged after the speech, noting that most of the work is done by non-governmental bodies rather than governments.
Obama has attended the conference every year he has been president and Romney, towards the end of his own speech, said: "A year from now, I hope to return to this meeting as president."
If he had delivered speeches throughout the year with the same apparent conviction as he did at the Clinton conference, he might stand a more realistic chance of fulfilling that hope.
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