If we imagine that there is no air resistance, the only factor that would be different for the two objects is the gravitational attraction between the Earth and the objects.
Both the hammer and the feather would experience the same acceleration due to gravity (approximately 9.81 m/s²), and they would fall at the same rate, meaning they would have the same velocity and take the same amount of time to fall. However, their masses are different, which results in different gravitational forces acting on them (F = m * g), where F is the gravitational force, m is the mass of the object, and g is the acceleration due to gravity. However, with no air resistance, they would still fall together.
Thus, the difference lies in the gravitational force experienced by each object, but when considering motion without air resistance, the key point is that they will fall at the same rate. Therefore, if you had to pick one answer based on the context of the question, it might refer to the gravitational attraction, as it is defined by the mass of the objects. However, in a practical sense of motion, there are no differences during the fall without air resistance.