Bill McGowan is the founder and CEO of Clarity Media Group , a global communications coaching firm based in New York. He is the author of "Pitch Perfect: How to Say It Right the First Time, Every Time." Follow him on Twitter @BillMcGowan22 . Juliana Silva is a strategic communications adviser at Clarity. The views expressed in this commentary are solely those of the author. View more opinion articles on CNN.

(CNN) In the coming days, President Donald Trump is likely to continue making direct comparisons between the death of Islamic State leader Abu Bakr al-Baghdadi and the killing of Osama bin Laden eight years ago. After all, Trump's presidency seems in large part to be dictated by either undoing or trying to outdo what President Barack Obama accomplished.

When Trump announced Baghdadi's death Sunday morning, he risked diminishing the significance of the victory by engaging in his classic hyperbole. "This is the biggest one perhaps that we've ever captured," Trump said before later reiterating, "This is the biggest there is. This is the worst ever. Osama bin Laden was very big, but Osama bin Laden became big with the World Trade Center," going on to point out that Baghdadi said he had built "a country."

There are plenty of differences between the two successful operations, not the least of which is how each commander in chief communicated the victory to the American people. The contrast between Trump's announcement and the address Obama delivered in 2011 illustrates the huge disparity between their characters, and their communication styles.

If you recall, on the night President Obama announced the killing of Osama bin Laden, he framed the victory with the restraint and dignity befitting of American global leadership. There was no chest beating, no boastfulness and no intent to humiliate the adversary. In fact, when asked why he tried to keep the pictures of bin Laden's dead body under wraps, Obama said , "That's not who we are. We don't trot out this stuff as trophies. We don't need to spike the football."

Trump, on the other hand, has done a self-congratulatory end-zone dance in the wake of Baghdadi's death. Trump said, " He died like a dog. He died like a coward. " In describing Baghdadi's last moments before he was cornered by US forces, Trump said the ISIS leader was "whimpering and crying and screaming all the way" -- words he repeated multiple times throughout the subsequent news conference.

When reporters asked the President whether he heard the whimpering himself, Trump refused to elaborate, saying, "I don't want to talk about it," and went on to add that Baghdadi was "scared out of his mind."

No one will dispute that Baghdadi was a notoriously evil terrorist who deserved his ultimate fate. Hats off to the US special forces who made it happen. But the wisdom of showing restraint in victory has been championed among even the greatest and most ambitious of America's military leaders dating back to Gen. Douglas MacArthur who once wrote , "Build me a son, O Lord ... who will be proud and unbending in honest defeat, and humble and gentle in victory."

There was nothing gentle in this victory for Trump. National security experts have questioned whether Trump would share too many operational details of the raid, for fear that his desire to dramatize the operation in cinematic detail could pose a security risk for US forces.

Trump may have also been unwise in sharing humiliating descriptions of Baghdadi's final moments, considering that hundreds of ISIS soldiers have reportedly escaped prisons in northeast Syria when the Kurdish forces were busy defending themselves against attacks from Turkey in the wake of Trump's abrupt decision to withdraw American forces. To that dangerous army, Baghdadi can only achieve a higher status of martyrdom because of Trump's excessive boasting. President Obama, on the other hand, was quite intentional in showing restraint for fear of fueling jihadists' thirst for vengeance.

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Was this operation a great moment in America's war on terror? Of course. All those who contributed to Baghdadi's death deserve a tremendous amount of credit. But the President would have been well served by displaying the same level of dignity and restraint Barack Obama showed following bin Laden's death.