I have aiptasia in my tanks that have resisted eradication despite trying most every method mentioned above and in other forums. Peppermint shrimp worked for a while, Berghia were eaten by peppermint shrimp (expensive lesson). High powered laser was very satisfying way to fry them but not permanently. Aiptasia-X caused one visible aiptasia in my corner tank to multiply into thousands within a few months. Klein's butterfly and matted file fish did a decent job of killing accessible aiptasia. Much of my rock is Pukani which has deep crevices that the filefish and Klein's could not reach. Eventually, I learned the secret of getting copperbanded butterflys to survive in my tank (no quarantine in 2/2 tanks led to 100% survival, quarantine with a tank full of aged live rock was good for another).
The CBB in my 150g reef is aggressive and holds its own with larger tangs and the Klein's butterfly at feeding time. It has eradicated all visible aiptasia, including those that were deep in rock that the Klein's and filefish could not reach. However I have no illusions. There will definitely be aiptasia in the overflow, pipes and elsewhere so the fish will always have some to munch on.
I have a small CBB in my frag tank and it has eradicated all visible aiptasia there as well. I bought another relatively large CBB for my 75g corner tank but the much smaller Kleins' butterfly in that tank harassed it mercilessly for days until the CBB appeared nearly dead. After about a week, I took that CBB out and put into a new 40g frag tank with a powerhead and all of the excess live rock I had in my garage Brute. It has now settled in after about a month of peace and quiet. That rock previously had aiptasia before I put into the Brute, but I can't see any now. The fish is happy.
So the moral of the story is that the best method I have ever found is ongoing biological control with fish that like aiptasia. A healthy CBB can do the job on its own and is a beautiful addition to any tank. Klein's are a mixed bag. Most eat aiptasia but the one in my 150g is a serious coral muncher. I had to move all of the fleshy corals (acans, pectinia, scolymia, trachys) to the frag tank where they have all recovered. The CBB in that tank doesn't bother any of them.