You can fly two different types of Copters. The civvie copter is basically free, and has a gatling gun and a few bombs. The gunship carries all that, plus missiles and rockets.
The primary weapon of the civvie copter is its gun. Given time or luck, this weapon can take out vehicles and other copters. Bombs back up the gun. As a last resort, the Civvie is cheap enough to employ suicide tactics, and ram the enemy. If the target is a gunship or AA gun, this can sometimes work to your advantage. However, if you die without taking out your target, you give the opponent free reign to plunder your territory while you're back at base waiting for a new helicopter to warm up.
The gunship's extra weapons give it formidable ranged striking power. Missiles can harass enemy copters 4 screens away. Rockets can decimate convoys from the same distance. With its large supply of ordnance, the gunship can spend more time in the thick of battle, and less time flying home to refuel. If you're skilled enough to be able to refuel one or two times before getting killed, then the gunship is well worth the expensive sticker price.
Note: These numbers are accurate for Copter Commander 1.0. New numbers are used in 2.0, and two new playable vehicles are added.