I haven't checked this myself but I'm told the pistol rounds actually can go slower because of the drag from the longer barrel. The only advantage to the carbine is increased accuracy
This is partially true. If the powder is still burning, the bullet can still pick up velocity from being inside a barrel. If you get a fireball, the powder is still burning outside the barrel. If the powder is finished burning but is still expanding with a force greater than the friction caused by the contact of the bullet and the barrel, velocity will increase, albeit slower than if the powder were still burning and expanding rapidly. Once the force from the expansion of the powder gasses drops below the friction of the bullet/barrel contact, the bullet will lose velocity.
The longer sight radius will allow increased accuracy, as has been pointed out.
The longer barrel will also cut down on muzzle blast. This may seem insignificant with 9mm and .45 ACP, but you can exaggerate it and see what I mean. Load some 9mm ammo with Blue Dot (use data from a reputable source) and shoot it out of a 4.25" or even a 5" handgun. Then fire the same ammo out of a carbine. I specifically mention Blue Dot because I happen to know it to be a loud powder out of the 9mm handgun.
Also, long guns are generally easier to control in rapid fire, which may or may not be a concern of yours.
