The 1968 Gun Control Act.
The FFL's are kept by the dealer and can be accessed by law enforcement people by going to the dealer you purchased the weapon from and requesting to see them.
They only give the name and address of who they sold them to. They do not keep track of subsequent transfers between private individuals.
If you bought such a weapon through an FFl dealer, with a lot of effort, the "Authorities" can trace that gun to you. All they can then do is ask who you sold or gave the gun to.
It goes like this.
The Authorities have a firearm they wish to trace.
From it's serial number, they go to the manufacturer, and find which FFL dealer the firearm was shipped to. From him they get to whom he sold the firearm. They then attempt to locate that individual, and ask him to whom they sold or gave the firearm. If it goes beyond one or two private transactions, the effort to trace a firearm becomes huge and the success rate becomes much lower.
In a registration scheme, there will be a central data base where all firearms are registered, with names and addresses of owners. Private transactions will be forbidden, as unregistered transactions would defeat the purpose of registration.
Much less effort, and it makes checking up on who has a firearm, much simpler. It would also make seizing guns much easier, if it ever came to that.
Currently, it makes it difficult to trace a weapon unless it is of late manufacture, or very important to do so.