With a 12-6 curve the harder you can throw it the better within reasonable limits. The harder you can throw the curve the closer you can come to releasing it level or ideally even slightly downwards if you could throw it hard enough to do so and still be a strike. That will result in the curve moving downwards faster as it crosses the plate.
When a curve is released upwards part of the time spent going towards the plate is used up in overcoming the upwards velocity and it ends up having less time to break down than if it were thrown harder and released without upward velocity.
The reality is that most curves are released with some upwards velocity and the difference between a hanging curve and a sharp breaking curve is simply that the hanging curve was released with a bit more upwards velocity than normal.
The other thing to remember is that part of the effectiveness of a curve is the change of speed relative to the fastball. That is why Oswalt's relatively slow curve can be so effective.