The photo shows the six men, all in dark suits or military uniform, posing for the camera and staring straight forward with stern expressions as they sit around a table.
The presidential seal gleams on the wall over Mr Trump’s head.
In this unposed scene, 13 faces are fully or partially visible in the crowded tableau.
Mr Obama, wearing a polo shirt and light coat, is hunched forward and perched on a folding chair slightly off centre.
The Trump photo, with the president in the centre and looking severe, is more formal and captures the current president’s interest in conveying the power and grandeur of his office.
It also reflects the tight circle of advisers from whom he solicits advice.
To his right are national security adviser Robert O’Brien, Vice President Mike Pence and defence secretary Mark Esper.
To his left are General Mark Milley, chairman of the Joint Chiefs of Staff, and Brigadier General Marcus Evans, the Pentagon’s deputy director for special operations and counter-terrorism.
The jumble of ethernet cables, legal pads and computers covering the boardroom table stands in sharp contrast to the formality of the moment.
The less formal Obama photo from 2011 crackles with suspense as the president’s team monitors the raid where Navy Seals killed bin Laden in a compound in Abbottabad, Pakistan.
The room is so crowded the presidential seal on the wall is barely visible.
Seated next to Mr Obama are Brigadier General Marshall Webb, who was communicating with the Seals commander Admiral William McRaven, who was in Afghanistan overseeing the covert special operations team that stormed the compound.
In the back of the room, Deputy Secretary of State Anthony Blinken can be seen peeking around the taller White House chief of staff Bill Daley to get a better view of the scene unfolding on a video monitor.
The packed room seems to reflect Mr Obama’s more expansive team of advisers and his interest in receiving a broad array of opinions.
“This,” he said, is “the biggest there is”.