Unlike the Falconet which it replaces, the Organ Gun hits multiple times at an enemy target to mimic the Falconet's damage.
While it's slightly cheaper than the Falconet and only costs 4 population, the Organ Gun has less health and damage penalty modifiers against many targets, while Falconet has damage boosting modifiers instead. Organ Guns are still useful in clearing out clumps of units, as Falconets can occasionally leave a few units behind because of their single cannon fire compared to a burst from an Organ Gun. Also, switching from Limber mode to Bombard mode and vice versa is faster with the Organ Gun.
"Also called a ribauldequin, this Renaissance-era gun's multiple iron barrels line up side by side. These small caliber (for artillery) projectiles were meant to be fired at the same time, creating a wave of fearsome iron that could tear ranks of enemy foot and cavalry soldiers apart."