This is literally untrue. 9mm ammo comes out of a longer barrel at higher velocity than out of a shorter.

http://www.ballisticsbytheinch.com/9luger.html

Velocity isn't really what you care about though. I understand the point you're trying to make, but that table really points out that the type of the round you're using has a greater effect on velocity than the barrel length itself. The linked muzzle energy plot, which is what you really care about, shows this quite well, where we stay fairly stable for all tested rounds and fall off significantly at barrel lengths shorter than 7".

Muzzle energy is defined as the bullet's kinetic energy upon exit, which is proportional to the square of velocity, which means barrel length necessarily affects muzzle energy more than muzzle velocity.

From quick Google searches, 9mm pistol barrels are around 4-5 inches long, 9mm rifles around 16". This has a major impact on muzzle velocity, and an even greater impact on muzzle energy.

But it's still reliant on trigger pull. How quickly you shoot rounds is roughly similar, depending on the reset trigger of the gun. In some cases you get more rounds out quicker from a pistol, they might not have the same velocity or accuracy however.

Edit: In other words I'm talking about rate of bullets fired per second, and not how fast they leave the clip / magazine which is what you're talking about.