The terrorist rampage at a Paris satirical magazine left the West reeling, but the attack was also the latest salvo in a lesser known fight, the public relations war between Al Qaeda and the Islamic State in which the prizes are funds from extremist benefactors around the globe and Muslim radical conscripts ready to kill and die on command.

Friday's claim from Al Qaeda on the Arabian Peninsula (AQAP) that it had directed the jihadist brothers, whose commando-style raid Wednesday left 12 dead at Charlie Hebdo, would appear to be a coup for the older and more established terror network, which for much of 2014 was overshadowed as Islamic State gained momentum. 

Al Qaeda's prominence among terrorist groups, undisputed in the years following 9/11, had been largely eclipsed as the newer group, also known as ISIS, seized territory in Iraq and Syria and carried out a series of high-profile beheadings that elevated its bloody brand. The Paris operation gives Al Qaeda's relevance a new boost, said Steve Emerson, executive director of the Investigative Project on Terrorism.

"It will accrue to their positive development in terms of financing, reputation and all that," Emerson said. "And there'll probably be a brigade named in the brothers' memory."

'Instead of one major terrorist group to be concerned about – there are now two serious threats. This also means more resources will be needed'

- Steve Stalinsky, MEMRI

French-born brothers Cherif and Said Kouachi were killed Friday in the culmination of a massive manhunt when French police stormed a printing plant 25 miles northeast of Paris where they had holed up. They reportedly told victims during Wednesday's attack on Charlie Hebdo they were with Al Qaeda, and Fox News subsequently reported that at least one of the brothers had traveled to Yemen and been in contact with terrorist training camp leaders there. 

The claim of responsibility, from one of AQAP’s top Shariah officials, Harith bin Ghazi al-Nadhari, removed any lingering questions about who was behind the shocking attack.

"Some of the sons of France were disrespectful to the prophets of Allah," Al-Nadhari, said in a speech first reported by the Washington-based SITE Intelligence Group. "So a group from among the believing soldiers of Allah marched unto them, then they taught them respect and the limit of the freedom of expression."

AQAP is hoping to reclaim the mantle of the international jihadi cause for Al Qaeda, said Steve Stalinsky, executive director of U.S.-based Middle East Research Institute (MEMRI), which monitors and analyzes jihadist and other communications. Charlie Hebdo had long angered Muslim extremists throughout the world by publishing demeaning caricatures of Prophet Muhammed, and terror groups and religious leaders had called for the death of its cartoonists.

FULL COVERAGE: Islamic Terror Massacre in Paris

It was, to Muslim extremists everywhere, a high-value target.

Stalinsky said he expects Al Qaeda on the Arabian Peninsula to fully maximize its success by putting out more claims and videos emphasizing its links to the brothers.“AQAP is notorious for putting out videos later, and they did that with the Underwear Bomber,” he said, referring to Umar Farouk Abdulmutallab, who was convicted and is in prison for his failed attempt to detonate plastic explosives hidden in his underwear on a U.S.-bound flight on Christmas Day, 2009.

On Thursday, a cleric at a Mosul mosque reportedly claimed ISIS was responsible for the Paris attack, but there appears to be no corroboration for that.  Elsewhere within ISIS, the blow struck in France appears to have earned respect. ISIS fighter Abu Mussab of Syria told Reuters that the Paris gunmen were "on the path of the emir (ISIS leader Al-Baghdadi) .... and our Sheikh Usama," a statement which also served as a calculated swipe at Al Qaeda by elevating Al-Baghdadi to equal status with dead Al Qaeda leader Usama Bin Laden.

The competition between the world's most feared terrorist groups is less than a year old. ISIS was an affiliate of Al Qaeda before their February, 2014 split. The decoupling was driven by the disapproval of ISIS tactics by Al Qaeda leader Ayman Al-Zawhiri, who ordered the upstart terrorist army out of Syria.

"ISIS 'is not a branch of the Al Qaeda group . . . does not have an organizational relationship with it and [Al-Qaeda] is not the group responsible for their actions," Al Qaeda's General Command said in a statement, marking the first and only time the leadership formally repudiated an affiliate.

But instead of leaving, ISIS leader Abu Bakr Al-Baghdadi pronounced himself an "emir," and declared a caliphate – or Islamic State – in the large swath of ISIS-controlled land that has effectively blurred much of the Syrian border with Iraq. Al-Baghdadi also called on Muslims throughout the world to swear loyalty to him. In the ensuing months, ISIS thrived as it seized oil fields and an Iraqi central bank, humiliated Iraq's army and brought cities and villages populated by millions under its control. That success brought an endless stream of foreign fighters into Syria and Iraq to sign on with the terror group.

Al-Baghdadi more recently went after AQAP, Al Qaeda's Yemen-based affiliate, after a jihadist group there pledged its loyalty to him. Al-Baghdadi accepted the declaration, and declared Yemen a new province of his caliphate. AQAP risked being overshadowed in its own back yard as ISIS engaged the Yemeni army and the adversarial Yemeni Shia insurgency known as the Houthis, and incurred sympathy-inducing American drone strikes. Just last month, ISIS proudly announced the death of one of its members, in Yemen, calling Humam Al-Ta'zi, "the first martyr of the [Islamic] State to die upon Yemeni soil."

"Despite the AQAP leadership's efforts to halt ISIS's expansion in Yemen, it seems that the organization is successfully recruiting new fighters and activists," MEMRI says in an analysis – Changing Dynamics in the Global Jihad Movement – released to FoxNews.com.

With the expansion into Yemen, where Al Qaeda operates numerous and sophisticated terror training camps that prepare fighters for war and terror missions, ISIS was taking on Al Qaeda's most potent affiliate on its home turf.

While the two groups have generally stopped short of killing each other, experts warn that as long as the competition is one of one-upmanship - competing over who can best strike at the common enemy - the rivalry’s real losers are the west. And American and other Western-born jihadi sympathizers have choices for joining Islamic extremist causes.

"Instead of one major terrorist group to be concerned about – there are now two serious threats. This also means more resources will be needed," Stalinsky said.

Both groups are looking to amplify their appeal to what Joseph Braude, a Middle East specialist as senior fellow at the Foreign Policy Research Institute in Philadelphia, called the "disaffected youth" of the world who are ripe for radicalization. Each successful attack and every headline one generates can help their cause, experts said. The West needs to answer with the help of Muslims who reject the extremist orthodoxy.

"The long-term strategy needs to include a proactive approach to fostering moderate elements in the Muslim world," Braude told FoxNews.com. "If we don't… these groups will continue to proliferate and metastasize."

Jonathan Schanzer, vice president for research at the Foundation for Defense of Democracies, said the two groups will continue to compete for terrorism market share, but for the West, the danger remains the same - "the overall appeal of militant Islam."

"We will see the tide change in favor of one group or another, but I think it is a distinction without much of a difference," he said.

Steven Edwards is a New York-based journalist. Follow him on Twitter @stevenmedwards