Obama said in his foreign policy speech last week that the prime threat comes not from al Qaeda's core leadership, but from affiliates and extremists with their sights trained on targets in the Middle East and Africa, where they are based. This lessens the possibility of large-scale 9/11-type attacks against America, the president said.
"But it heightens the danger of US personnel overseas being attacked, as we saw in Benghazi," he said, referring to the September 2012 attack on a US diplomatic outpost in Libya that killed the US ambassador and three other Americans.
Experts argue that this restructured al Qaeda is perhaps even stronger than it has been in recent years, and that the potential for attacks on US soil endures.
"We have never been on a path to strategically defeat al Qaeda. All we've been able to do is suppress some of its tactical abilities. But strategically, we have never had an effective way of taking it on. That's why it continues to mutate, adapt and evolve to get stronger," said David Sedney, former deputy assistant secretary of defense for Afghanistan, Pakistan and Central Asia.
Decentralisation does not mean weakness, he said.
"I think Americans think al Qaeda is no longer a threat - that Osama bin Laden's death means al-Qaida is not a big thing anymore," Sedney said.
He believes al Qaeda is gaining strength in Pakistan, is stronger in Iraq than it was three or four years ago and is stronger in Syria than it was a year or two ago.
"This is a fight about ideology. Al Qaeda is not this leader or that leader or this group or that group," he said.
The experts say al Qaeda today looks less like a wheel with spokes and more like a spider web stringing together like-minded groups. But they believe there are several reasons that those who track al Qaeda warn against complacency.
While bin Laden was killed and his leadership team heavily damaged by U.S. drone strikes in Pakistan, the drawdown of American forces in neighboring Afghanistan will dry up field intelligence and restrict the effectiveness of US counterterrorism operations. There is a worry that a pullback could allow al-Qaida to regroup.
Moreover, they worry about the thousands of foreign fighters flocking to the civil war in Syria. The has emboldened the al Qaeda breakaway group known as the Islamic State of Iraq and the Levant to expand its cross-border operations into neighboring countries such as Iraq.
US officials also are concerned about Westerners who have joined the Syrian fight because they may be recruited to return home and conduct attacks.
When the US counterterrorism strategy was conceived, it was thought that if al Qaeda's core leadership was dismantled or killed, then affiliated groups would simply become localized threats, said Katherine Zimmerman of the conservative American Enterprise Institute.
At that time, there wasn't a network of connections among all the groups, said Zimmerman, who specializes in the Yemen-based group, al Qaeda in the Arabian Peninsula, or AQAP, and al Qaeda's affiliate in Somalia, al-Shabab.
"As the network has become more decentralized, it's become much more reliant on these human relationships and the sharing of resources, advice and fighters, which means that you no longer need bin Laden sitting in Pakistan dispersing cash to various affiliates," Zimmerman said. "They have developed their own sources. ... You can't simply pound on part of the network and expect to see results."
Tom Joscelyn, a senior fellow at the Foundation for Defense of Democracies and senior editor of The Long War Journal, a website that tracks how al Qaeda and its affiliates operate around the globe, said he thinks the Bush and Obama administrations mistakenly defined al-Qaida as a top-down pyramid with a hierarchal structure - that "if you sort of lop off the top of the pyramid, the whole thing crumbles."
Al Qaeda leaders have scattered to other parts of the world, he said, noting that al Qaeda in the Arabian Peninsula is headed by a former aide to bin Laden, who is now general manager of al Qaeda globally.
More recently, the treasury department penalized a senior al Qaeda operative on the terrorist network's military committee who relocated from Pakistan to Syria and is involved with a group plotting against Western targets, he said. US officials have tracked communication traffic going back and forth between Syria and Pakistan and Afghanistan, he said.
"This shows, to my mind, that we're not dealing with this sort of discrete core entity in Pakistan and Afghanistan that can be droned to death, but in fact an international network that poses a lot graver challenges," Joscelyn said.
While Obama is keen to burnish his legacy as a president who ended US involvement in the wars in Afghanistan and Iraq and killed bin Laden, even he has softened his rhetoric on terrorism.
Two years ago, on a trip to Afghanistan, Obama said, "The goal that I set - to defeat al Qaeda, and deny it a chance to rebuild - is within reach."
His administration's most recent terrorism report, released by the State Department in late April, uses a less definitive voice.
"The al Qaeda core's vastly reduced influence became far more evident in 2013," the report said. "Al Qaeda leader (Ayman) al-Zawahiri was rebuffed in his attempts to mediate a dispute among al Qaeda affiliates operating in Syria, with the Islamic State of Iraq and the Levant publicly dissociating their group from al Qaeda."
Michael Sheehan, a terrorism expert at the US Military Academy at West Point, New York, said the top two groups he fears could attack the U.S. are "al Qaeda central" in Afghanistan and Pakistan and AQAP, which has attempted several attacks on the United States, including a failed airline bombing on Christmas Day in 2009 and the attempted bombing of US-bound cargo planes in October 2010.
"The other organizations right now - although potentially very, very problematic - are currently focused on the local fight," said Sheehan, the Obama administration's former assistant undersecretary of defense for special operations and low-intensity conflict. "Whether eventually they shift to Europe first, then the US, we'll see. But certainly a potential is there."