It is an individual choice. The synthetic is what most doctors prescribe, but if you have a problem with it, then suggest your doctor try the armour.
Because I no longer have a thryoid my endo wants me on the synthetic. In addition, she wants it to be a brand name. Supposedly, that has the most consistency of anything out there. She also wants me to take it in a consistent manner and wait two hours before eating or drinking. This way if anything starts going off the beam, she can rule out it possibly being the med and investigate other areas. My first inclination was to go for something 'natural' but her thinking made sense to me so I've gone with it.
Good luck.
Regardless what you choose - you will know in time if it is right - just remember you have options - Don't be quick to judge or switch - give whatever a really good try and if it doesn't seem right - you will know. :)