Differs from state to state regulations, situation to situation and a person's view and ability to "influence" their "residency" if one location is preferable to another.
Having moved through many states, some temporary, some more permanent, sometimes multiple homes and multiple vehicles in different states, I can say that there is no universal answer and virtually noone cares save for the cops if you get pulled over. (Insurance companies care, but sometimes they wouldn't even modify our policy until it renewed. I'd just notify them and let them decide where they want to write it to.)
And having gone through that scenario multiple times, as long as you have a reasonable explanation for the officer, it's never been a problem for me. I've actually presented 3 different state drivers license, license plates and insurance and not an issue as long as everything is valid and checks out.
For the OP, if GA is cheaper, it's a slam dunk because that appears to be your resident state (not to be confused with tax home if it matters). If TN is cheaper or more convenient, and you can produce the right documentation to get it titled and registered there then do it there.