I use both marines and paratroopers as stack defenders until my army is fully able to move 2 spaces. Against anything that isn't gunpowder, they do better than infantry. My enemies tend to us a crap-ton of cavalry, so it works out well. Paratroopers have been useful as a mobile defense force when I'm rapidly advancing. So I can use airports to put one unit in, but then paradrop as many paratroopers as are in range... This is nice when the enemy has railroads. A single defender, even a good one, is unlikely to cut it and I don't want to leave my stack of doom there for more than a turn. Then once the city is no longer in revolt I can move the paratroopers away to defend the next city, and move them back if it becomes threatened. I also use paratroopers for resource denial: Paradrop onto their oil/uranium, pillage it, fortify there until it's no longer in their borders. Works better than bombers because the enemy can just use all their workers to rebuild unless you have a unit parked on it. Paratroopers are also great on archipelago maps where they can island hop without using ships.
The only way I've used marines that is more effective than paratroopers is when I'm attacking a single tile island defended by a machine gun. If it's not a single-tile island, then you just use artillery first.