If the two objects are identical in shape the initial drag force on both are equal since drag is a function of the shape and velocity. However, since the two objects have different mass the resultant deceleration rate is different, and the heavier object will decelerate slower than the lighter object, and this deceleration rate difference will in effect change the drag force (since drag force is proportional to velocity squared). In this sense, the two objects will likely not hit the ground at exactly the same time. The kinematic equation governing motion of the object is:
$d^2x/dt^2 = g - 1/2\rho AC_d(dx/dt)^2/m_{object}$
Note that $C_d$ is a function of the Reynolds number which will vary with velocity but depending on your velocity range and shape it may be treated as a constant. Solving the above equation will give x(t) and given the height you drop from you can find the time it takes for each object to impact the ground.
In a vacuum both objects will hit the ground at the same time.