I am not a lawyer, but this is as good as I can tell you.
There are no downs to it that I know of. No taxes needed. If you die, the NFA item gets passed on to whomever you elected in your trust, free of taxation I believe. (you would list your kids, wife etc. as recipient when you create the trust).
You would not change names on the trust if you were selling the item. The buyer would have to decide which method he or she wanted to use, and file for themselves.