In the scenario described, where there is no air resistance, the value that will be different for the two objects—the hammer and the feather—is the gravitational attraction between the Earth and the objects.
However, it's important to note that while the gravitational force acting on both objects is different due to their different masses (the gravitational force is equal to mass times the acceleration due to gravity), in a vacuum where air resistance is absent, both objects will fall at the same rate and will hit the ground at the same time. They will have the same acceleration (due to gravity) and will fall the same distance in the same amount of time.
So, strictly speaking, while the gravitational attraction is different because it depends on the mass, it affects the fall in exactly the same way for both if we only consider gravitational effects. Therefore, in terms of their motion (velocity, time to fall), there would be no difference; they would fall identically. If we consider strictly the effects of gravity in terms of force, then the gravitational attraction is the answer.
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