Nature Throid and Armour are basically the same. The binders and fillers are different and Nature Throid is suppose to be hypoallergenic for people who may have a reaction to the binders or fillers in Armour.
Some people do better on Armour, some do better on Nature Throid. I have tried both. I prefer Nature Throid, Armour made me feel odd and I got leg cramps on it. I also take a synthetic called Unithroid. Many people cannot tolerate just the natural and need a synthetic to keep the T4 level optimal.

The dessicated thyroid meds are from pig because their thyroid is closest to the human thyroid. It does however have more T3 than we generally need therefore the added synthetic T4 along with the natural works well for many people.

Be glad your dr wants to use the natural. Many won't prescribe it. I hope he is open to adding a synthetic if the natural has too much T3 for you.