PARIS — In 2007, Belgian police were keeping close watch on Malika el-Aroud, a fierce al-Qaida ideologue whose dark eyes smoldered above her veil.

The Moroccan-born Aroud had met Osama bin Laden while living in al-Qaida’s stronghold in Afghanistan. She gained exalted status when her husband posed as a journalist to blow up the renowned Ahmed Shah Massoud, the chief of the anti-Taliban Northern Alliance, just two days before the Sept. 11 attacks.

Aroud later returned to Europe, remarried and started an Islamist website that attracted a group of French and Belgian extremists. Led by her second husband, Moez Garsallaoui, half-a-dozen of them went to Waziristan, where they joined several thousand al-Qaida fighters, including a Latino convert from Long Island, learned to make bombs and plotted against the West with terrorist kingpins.

The authorities — American, Belgian, French, Swiss, Italian, Turkish — were all over them.

U.S. surveillance had tracked their radicalization, their emails from Pakistan, even calls made to their mothers before they trudged through snowy Iranian mountains. An intercepted photo that Garsallaoui sent his wife showed him holding a grenade launcher. He claimed to have killed U.S. soldiers in Afghanistan and described his escape from a missile strike: “I came close to dying.”

The militants took precautions, changing laptops and using Internet cafes. But they were no match for top-secret, real-time NSA intercepts. Some of the monitoring was approved by the Foreign Intelligence Surveillance Act.

“We were inside their computers,” a source said.

As debate rages in the United States about the National Security Agency’s sweeping data-mining programs, I’ve been on a reporting trip overseas, where I’ve been talking to sources about the controversy and how differing U.S. and European approaches to counterterrorism can complement each other.

On Tuesday, NSA Director Gen. Keith Alexander, told a congressional committee that his agency’s surveillance programs helped stop more than 50 terror plots in the U.S. and abroad. Five years ago, I was based in Europe covering terrorism, running from one attack or aborted plot to another. As the Brussels investigation shows, these cases frequently combined the high-tech reach of the U.S. counterterror apparatus with the street skills of foreign agencies.

In November 2008, Pakistani and U.S. agents swooped into Kandahar and nabbed Bryant Neal Viñas, the convert from Long Island and al-Qaida militant. He cooperated with the FBI, admitting that he discussed an attack on the Long Island Rail Road with top al-Qaida figures.

Days later, a drone strike killed Rashid Rauf, a Pakistani-British operative who helped plan the London transport bombings and the “liquid bomb” plot to blow up planes in 2006. Three Belgian and French militants returned home, where police arrested them after intercepts picked up menacing chatter.

Viñas pleaded guilty. Aroud went to prison, and investigators believe her second husband Garsallaoui died in the land of jihad.

Other cases benefited from close cooperation. In Germany in 2007, U.S. monitoring detected a suspect checking the draft file of an email box at an Internet cafe in Stuttgart. Armed with that lead, German security services deployed surveillance at numerous Internet cafes in the city. The investigation resulted in the dismantling of a Pakistan-trained group plotting to attack U.S. military targets in Germany.

As several European sources told me, if an extremist in Marseilles was talking about nefarious activities with an extremist in Geneva over the Internet, chances were good that U.S. intelligence agencies would find out and inform the French and Swiss. Not because of sources on the ground, but because U.S. agencies could detect the communications through computer servers in the United States.

The reaction here to the U.S. debate has been bemused.

European terrorist hunters seem surprised that the revelation of the NSA data-monitoring programs is big news. The technological capacities of U.S. agencies have been an integral component of dramatically improved teamwork against terrorism during the past decade.

“In the fight against terrorism, intelligence-sharing is essential,” said Jean-Louis Bruguière, who served for more than two decades as a top French antiterror magistrate before retiring in 2007. (He declined to discuss the NSA’s role in investigations.) “Cooperation with American services has always been trusting and excellent.”

At the same time, some European experts see the furor as a sign that the strengths of the American giant intertwine with its weaknesses. U.S. agencies devote huge resources to sophisticated technology to the detriment of analysis and human spying, they say. As a result, they say, U.S. agencies sometimes appear overwhelmed by the sheer volume of information.

“The problem is not collecting information, it’s understanding it,” said Alain Bauer, a well-connected French criminologist who has served as a presidential adviser. “What is the sense of such programs? They are too big. They will not work. We are a former colonial empire. We know the value of human intelligence. It is more efficient and less expensive than technological fetishism. Fortunately, we do not have enough money to do it the other way.”

Spy agencies such as France’s DCRI and Britain’s MI5 have long experience cultivating human sources. In early 2008, Spain’s Civil Guard broke up a plot to bomb the Barcelona subway thanks to a French informant. He was a Pakistani who infiltrated the network in the training camps and traveled with the would-be bombers to Spain. He sounded the alarm when the attack seemed imminent.

I have met many American agents who are adept at operating in foreign cultures. Diversity adds value. U.S. agencies can send Pakistani-Americans to work in Islamabad and Mexican-born officers to Mexico City.

Nonetheless, U.S. agencies have less experience with Islamic terrorism at home. That’s partly the result of a good thing: Overall, the United States does a better job than most countries of integrating immigrants, including those of Muslim heritage.

In Europe, decades of religious, nationalist and political violence have bred an arsenal of counterterror tools. The security forces have developed extensive knowledge of large Muslim populations with subgroups involved in crime, extremism or both. The security forces recruit informants, interpreters, analysts and investigators from those communities.

As Bruguière pointed out, France staved off Islamic terrorist violence from 1996 to 2012, when an extremist named Mohamed Merah killed seven people in shooting attacks on French soldiers and a Jewish school in Toulouse.

“Gathering intelligence is the linchpin of the fight against terrorism,” Bruguière said. “In France, the emphasis is on humint [human intelligence]. But technological intelligence has not been neglected, in fact it has been notably reinforced.”

To be sure, the Europeans have experienced failures. The transport bombings in London in 2005 and Madrid in 2004 took place despite the fact that some of the suspects had been under surveillance.

Though sectors of the European media and public complain about the prospect that the NSA might spy on them, at home they are accustomed to invasive practices. In Italy, electronic surveillance routinely targets tens of thousands of citizens. Italian law has made it easy to wiretap and hard to do undercover operations. In 2010, the Italian justice ministry reported that law enforcement had monitored more than 112,000 phones the previous year.

In France, political parties across the spectrum accept the existence of a vast grid of domestic spying. In 2004, I went to see a police intelligence chief in a French city. It was a Thursday in August. I wanted to know if he was concerned that a newly announced ban on Islamic headscarves in schools might incite unrest when the academic year began.

“I don’t expect any problems,” he said. “But tomorrow is Friday. It’s a good day to gauge the mood based on the sermons at the mosques, especially the fundamentalist ones. Come back tomorrow afternoon, and I will have a better idea.”

The next day he repeated his assessment, which was accurate. It was clear that the police monitored — presumably with a mix of human and technical methods — Muslim houses of worship, including the clandestine prayer rooms in basements and garages frequented by hard-core extremists. Each week, the intelligence web collected and analyzed Friday sermons and generated a report that was on the chief’s desk in a few hours.

The U.S. reaction to NSA data mining strikes my European interlocutors as somewhat academic — a debate about potential rather than actual abuse. They don’t see a scandal.

“Something that is more dangerous to individual liberties and data protection than the secret American metadata programs, such as Echelon or PRISM,” said Bruguière, “is the insufficiently controlled commercial availability of innovative technological products such as social networks or the Google Earth and Google Street programs, which can be easily diverted toward criminal or terrorist ends.”

Some here see quite another problem: They think the U.S. intelligence community has overreacted to Islamic terrorism, acting as if the networks have the dimensions and discipline of Cold War-era state adversaries. That can cause excessive rigidity and secrecy.

A veteran European police investigator told me an anecdote. He once shared intelligence with a U.S. counterpart about a terrorism case. Some time later, he talked to the American official again. The conversation led him to believe that the U.S. agency had misunderstood or misinterpreted the intelligence.

The investigator recalled: “I told him that we needed to go over a couple of points. He said: ‘I can’t talk to you about it any further.’ I said, ‘But it’s about a lead we gave you.’ He told me: ‘Sorry, it doesn’t matter. It’s secret now.’”

The European investigator speaks Arabic and has spent years on the front lines. He says the U.S. emphasis on technology can be counterproductive, distancing the watchers from their target.

“In our work, there is no substitute for this,” he said, gesturing across a cafe table. “Face-to-face contact. Empathy.”

Before joining ProPublica, Sebastian Rotella worked at the Los Angeles Times, where he was named a Pulitzer Prize finalist in 2006 for his coverage of terrorism and Muslim communities in Europe.