Rate of motion, including falling, is determined by the second law of motion
v2 = v1 + a△t,
where v1 is initial velocity, v2 is final velocity after a period of time, t, and a is acceleration. Note that there is no mass quantity in this equation, indicating that the mass of an object is irrelevant to its motion in a frictionless environment.
Applying this to a falling object, presumably in free fall (no initial velocity), with a being the acceleration due to gravity, we see that - again in a frictionless environment - all objects will fall at the same rate (Galileo actually proved this).
However, in an environment where friction is present, different objects will fall at different rates, depending on the degree to which friction opposes their motion. Air resistance, a form of friction known as fluid drag, is a function of surface area; the greater the surface area, the greater the drag, and hence the greater the resistance to motion.
The issue is a little more complicated than this, but, in a nutshell, objects with greater surface area will experience greater fluid drag, which would tend to cause them to fall more slowly.