I've heard that its a difference in the thickness of the metal primer case. Supposedly, if you use a rifle primer in a pistol round, you may get light strikes that won't fire the round. If you use a pistol primer in a rifle cartridge, the primer may be crushed by the firing pin.
This is from the American Rifleman.
It may be small, but without the little bang of the primer, there is no big bang of the gun.
www.americanrifleman.org
Pistol primers have thinner and somewhat softer primer cups than their rifle counterparts. Small pistol and rifle primers utilize a cup 0.175" in diameter, while large pistol and rifle primers measure 0.210" across. Large rifle primers are 0.008" thicker than a large pistol primer.
Here's a guy who did an experiment replacing pistol primers with rifle primers.
www.24hourcampfire.com