In many ways, I like the Civ3 helicopter. Helicopters can't really exist away from base indefinately. Here is what I would have done to improve it, though.
1. Allow it to pick up units (simple suggestion to give a helicopter more of a use).
2. Allow the creation of Attack Helicopters using the C3C "Stealth Attack" feature. Helicopters can fly over the heads of enemy troops and be much more precise in their targets. They were dispised by the Vietnamese army because they could shoot from above, negating what defenses they created. Also, in Operation Iraqi Freedom, Apaches were used at one point to minimize non-combatant casualties. For the negative side, they should be rediculously easy to shoot down for anyone who has some kind of AA).