Iodoral has a more dependable strength. Originally, I only used Lugol's but I switched.
But the day I switched to Iodoral I felt a disinct boost in mental energy and stamina. Iodoral spoiled me. Now I only use Lugol's solution for skin stuff.
Whatever Iodine you choose, be sure to take all the companion nutrients to get maximum absorption and detox. This web page applies to all reasons for taking iodine, not just breast disease.
See: http://www.breastcancerchoices.org/iprotocol