For the average aquarist, I think the Matted Filefish (aka Aiptasia Eating Filefish) is hard to beat for aiptasia control.
It often takes a small colony of peppermint shrimp to affect aiptasia, and after awhile they may become more interested in fish food - but if you can add sufficient quantities they will do a good job.
Berghia nudibranch may get eaten by your fish, and will die once the aiptasia are depleted - so they seem to be an expensive, short-term solution at best (though I have no direct knowledge using them)
The Copperband Butterfly is a beautiful fish, but many people seem to have trouble keeping them alive. They can also be expensive, may pick on corals or other inverts, and are fast enough to be difficult to catch if you need to remove them from your reef tank.
The Matted Filefish, or Aiptasia Eating Filefish, will live up to its name and has the extra bonus of being inexpensive, very easy to keep, and usually very easy to catch if you need to remove it. Their willingness to pick on coral varies, but they seem to prefer aiptasia and once aiptasia have been removed - the fish can be removed if desired. They are also ugly enough to be cool, imho.
Because of how the aiptasia reproduce, once you have them you will probably always have them. :mad2: