I have seen on the different rare ship weapons (green) that it says stuff like "enables aux ofline" and "enables engines offline" etc etc....
What does this mean?
That's cryptic being too lazy/busy to fix something they have known about for a week (I know this because mdarga clarified that description last week). All phasers have a very small chance to disable a random subsystem for a few seconds. So far though. I have only seen shields go down, but that might just be because that is the most observable subsystem. Anyways, that ability has nothing to do with being rare, even a common standard issue has that effect.
The rares have stuff like an accuracy boost, or a bonus to critical hits (damage or chance)