The following advice is just experiences from myself or other local club members at RRVR...
1. Peppermint Shrimp: These are hit and miss at best. Many stores sell Camel shrimp as peppermints as well so you need to make sure you get the right ones from the start. I wouldn't recommend them unless you like them as tank livestock in case they don't go for the aptasias. If starved I have heard they will become opportunistic and co after LPS and Zoa flesh.
2. Copper Banded Butterfly: These will eat aptasia, but will not always take to frozen food so they can succumb to starvation in captivity. Be ready to give it away to someone who has aptasia so it can be a traveling workhorse for area reefers. There is no guarantee it will get everything though and the process of ripping them apart to eat can actually worsen the situation.
3. Berghia: These things ONLY source of food is Aptasia. They will not eat anything else so when it is gone, they will die off. They readily reproduce in captivity and will expand their population based on the food source. However I have been told if their numbers get too great and you have too many of them die off at once, they can release a toxin that can wreak havoc on your system. If you go this route, be sure to spread the love within your local reefing community as this will make sure that when your aptasia is gone and your berghia population is also gone, you have a chance to get some back if the issue returns.
4. Joe's Juice/Aptasia-X: Chemically burning them away using these products does work, but only if you get the whole nem. If you miss a spot it will come back. The repetitive use of these can increase the PH of the tank a bit so you can only treat so much before you need to take a break. Also for what these products actually are, they get very expensive in the long run in a massive aptasia battle. You can do the same thing with a mixture of Kalkwasser (Mrs Wages Pickeling Lime) and RODI water and make your own "juice". One bag of Mrs Wages should last even the most heavily aptasia infested for at least a year.
5. Vinegar/Lemon Juice/Other Chemicals: This is basically the same as 4...
6. Majano wand: These are an interesting device. It is basically a low voltage transformer which uses the conductivity of the saltwater to cause a chemical reaction to burn off the pest. It works well if you can reach the whole pest. However, some of these devices are not made well and can let water into the copper wire core. We all know what copper does to tanks, so make sure you inspect the device well and make sure it meets your approval before using it in the tank.
7. Lasers: This is a very interesting and effective tool to kill off pests. However when used incorrectly can cause instant blindness in the user, bystanders, pets, and even the fish in the tank if the reflection goes the wrong way. If you go this route, make sure you get trained in the proper use of the laser and ALWAYS wear protective gear. If you can, keep all bystanders out of the vicinity to protect their vision. Use at your own risk and be safe...