Do I need a cordless screwdriver if I own a cordless drill?
The electric screwdriver can sometimes fit where a bulky drill cannot, e.g., electrical boxes.  Apart from that, the drill is a fine screwdriver (assuming it has a clutch, of course, but I have never seen a battery-powered drill that does not).

Don't get rid of your corded drill. Battery-powered drills, especially the cheap ones, are not powerful enough for serious drilling such as a 5/8-inch hole through a 4x4 or any hole through metal.