Question

What is the differences between the acceleration rate of objects on Earth versus objects in the vacuum of space?

Answer 1

In space objects will essentially accelerate faster given the same amount of applied force since there is no drag like there would be on Earth.

Answer 2

If by space, the question means actual space -- outside the range of any significant gravitational force -- then the acceleration of an object in space is ~0.

But if it means some vacuum on Earth, then what Shane_B said.