My preferred strategy at this point is to use a combination of burst laser and ion to keep enemies' weapons offline, however I seem to run into a lot of problems especially with higher level ships if they have drones. They tend to beat down my shields and if the opposing ship gets a good volley off it can really wreak havoc especially if I am dealing with a boarding party as well.
I have tried to keep drone control offline on the enemy ship but it doesn't work as well as weapons suppression (as above). I think this is mostly because drones come back online and begin attacking immediately after the system is repaired, as opposed to weapons needing to charge.
Is there any way to destroy or disable drones other than damaging/disabling the enemy drone control module?