Armour thyroid is the "natural" therapy from dessicated porcine thyroid gland while Synthroid is produced synthetically as levothyroxine. Armour thyroid contains both T3 and T4 while Synthroid only contains T4. There is debate on whether or not use of both or one is better. Synthroid came into use because it was standardized unlike the natural kind, which varied a lot from batch to batch. But it turns out that patients often don't like T4 alone as much as the natural T3/T4. A new synthetic T3/T4 is now on the market as Liotrix, but is expensive.
Reference
http://www.netwellness.uc.edu/question.cfm/24516.htm
