The Pistol Swords have unique combat animations, similar to the Dagger of Brutus and Vlad Tepes' Sword, that mainly consist of Edward paralyzing an enemy, then shooting them with the pistols, and/or impaling, then shooting.
Stat-wise in AC4, the Pistol Swords are identical to Officer's Rapiers.
Historically, the idea of a pistol sword is much less glamorous. The reality is that such a weapon would be too heavy from the added weight of a firearm, to be carried in one hand. A second deterring factor is that if held downwards, such as Edward does when idle, the lead balls used as ammunition would often fall out of the barrels of the pistols unless fixed with wax, or specialized locking breeches.