Gunships count as "mounted" units, so any unit with a bounus against mounted units, such as cavalry, have the same bonus against gunships. On the positive side, they have a large bonus versus tanks and modern armor, so they are much better anti-tank units than the ground based anti-tank soldier unit.
They also have a 4 tile movement range, which gains bonuses in movement on roads and railroads.
They cannot capture workers. If they move onto a tile with any enemy workers, the workers are destroyed.
Although they cannot get medic promos, if you upgrade a horse riding medic unit to a gunship, it keeps all its medic bonuses. So, by gettting, for example a cavalry unit, to medic 3 and then upgrading it to a gunship, you end up with a medic that can stay in a captured city to heal damaged assault uniits rapidly and then quickly overtake the main stack.
I always include a couple of combat promoted gunships with stacks of city raider tanks or modern armor. Any of the enemy gunships that attack the stack will face my gunships instead of my tanks.
They cannot capture cities. They can attack and destroy defending units but cannot move into the city until after a ground unit has done so and captured the city. Sometimes I will use them to kill the last few defenders and them move, perhaps the only ground unit unused in the stack, into the city, which then has no defenders, thereby capturing it. Then the gunships which still have moves left, due to their 4 tile movement factor, can move in and help defend against any counter attack.
They interact with non-gunship air units the same way as tanks, infantry, etc. In short, they cannot damage those units and are subject to the same damage as any other ground unit.