The term big 4 has been applied too so much over the years metal can't even claim to have come up with it, so whoever coined it first along with four thrash metal band names stole it from somewhere else anyway.
But as I've said before it really didn't mean that much to most of the metal heads I knew in Australia during the 80's. Maybe it has something to do with the term being stolen, maybe it just wasn't marketed that way. Either way the Big 4 of Thrash always seemed to mean more to American's than us, but it's the same for the Teutonic 4, we mostly knew them individually and for most of us Tankard and Destruction weren't in the same league as Sodom and Kreator.
I've seen all of the Big 4 in the early days, never as the big 4 because they all toured Australia individually. I've also seen Anthrax, Slayer and Megadeth since then but haven't seen Metallica live since AJFA.