In a spaceship accelerating at g, far from earth's gravity, how does the motion of a dropped ball compare with dropping one on earth?

On earth, the speed at which a ball falls depends on the distance at which you release it. If you release it in the same place, and at the same distance from the ground, the speed will be the same. While in a spacecraft with constant acceleration, if you repeat the process from the same distance from the ground, the ball will have more and more speed due to inertia. But of a spaceship with a constant speed, that can not be differentiated, this is called equivalence principle, but that's another story...

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