Hi Kate and welcome to Wags.
I think cast iron is superior due to the even heat distribution it offers. It is also very durable. These cast iron pieces can last several lifetimes with proper care. The seasoning on them can over time become as non-stick as any Teflon or other non-stick surface. In addition, you don't have the health concerns that can come with Teflon for example. The cast iron actually adds to the iron content the food prepared in it. The only limitations would be the preparation of acidic foods. They are also not good for food storage. I use it for most everything I cook.
As far as Tennessee cast iron goes, you have the only foundry still making cast iron cookware in the United States. Lodge cast iron out lasted Griswold, Wagner, Wapak, Favorite, and many others. I judge cast iron by the quality of the casting. I wouldn't say that the cast iron itself is different, but the quality and craftsmanship with which it was made differs quite a bit. The modern Lodge is not the quality of the older stuff because it is now automated. The old hand cast pieces are as smooth and finely cast as any you will find. I have many of their older pieces, but also have modern Lodge pieces as well. I use them all. I support Lodge and hope they continue to compete with the pieces made overseas.