I believe the difference here is the meaning between "capture" and "board." Capturing a ship consists of boarding the vessel and taking it over. Boarding a ship however, isn't necessarily concerned with capture of the craft, so in those cases, who cares what kind of state the vessel is left in, as long as you can board it and capture who or what you're looking for on it.
In the case of the movies, the Devastator obviously wasn't interested in capturing the Tantive IV, only boarding it and capturing the Princess and recovering the Death Star plans. The Devastator is also many times larger than a corvette and with strong shields, so it need not be concerned with taking out weapons systems, as it could take whatever the Tantive IV could dish out, even if it was firing on it during boarding maneuvers. A smaller boarding craft would definitely need to be worried about this though. If only the engines were taken out, a well armed vessel could very easily still defend itself from a boarding operation. They would also be useful against more fragile targets, such as shuttles and fighters. The Rebels in Empire on the other hand just wanted to knock a Star Destroyer out of commission for a long time so the transports could get away. These connotate two different uses of ion cannons, but they both share the common goal of taking out defenses, with the former for boarding purposes.
Ions should take out a craft for a long time, from a few hours to days, which is much longer than any can take in a game, unless you...edit in the status in the following mission, let's say. Ships should be able to repair themselves in most cases I think, but a specialized repair crew will obviously expedite the process.
I suggest splitting this thread into a separate discussion of ion cannons before it gets any further off topic.