The copperband butterflyfish will indeed eat Aiptasia but not nearly as enthusiastically as a filefish would. On the other hand a copperband butterfly fish certainly looks a lot better in a fish tank.
Unfortunately the copperband butterflyfish often does not fare well in a home aquarium and it is considered to be hard to maintain long term.
Some people have problem even feeding captive copperband butterflyfish, and various not always consistent advice can be found on the Internet. I do remember that copperband butterflyfish will eat mussels, clams, oysters, etc. that have been opened (i.e. eat the meat off the half shell), but other smaller fishfood is often recommended. Copperband butterflyfish will also pick various small worms from the rockwork so if you intend to keep those you probably should avoid getting a copperband butterflyfish.
I probably should not give advice on this topic as I was just as unsuccessful maintaining copperband butterflyfish long term as the next guy. The pictures above are not in my reef tank but of a specimen in the Toronto Zoo, where there is a a reef exhibit inside the Australasia Pavilion.
Buyer Beware: The Copperband Butterflyfish (Chelmon rostratus).
Copperband Butterfly Fish Chelmon rostratus.
ReefCorner: Copperband Butterflyfish – Chelmon rostratus.