There's a good answer for this actually.
1. Conceivably, it is easier to lift the man out of the Pumphandle then it is for a bodyslam, especially the whole putting the guy on the shoulders part. Easier when your hands are not between his legs. In a Pumphandle, you don't need to get your arm out from between the legs like you do with a Powerslam.
2. Kayfabe-wise, would you rather lift a guy using your right arm while bent to the side a bit (the left arm only supporting his head, not holding any weight) for a Powerslam, or would you rather lift a guy directly in front of you with both arms for a Pumphandle Slam? The latter is easier, especially for a smaller combatant.
3. When done to its fullest effect, The Pendulum-like nature of lifting the guy up then throwing him right back down would also create more impact. Much like swinging a Golf Club. A Powerslam does not create such an effect.
Most importantly:
4. Would you rather put your hand near your opponents privates for a Powerslam, or hold your opponents wrist a bit further away form the nether-regions?