The big 4 is just a marketing term and its based off of popularity and influence....if we're basing it on pure influence then it should be Metallica, Megadeth, Slayer, and Exodus at least IMO. Exodus is arguably the second most influential thrash band. Testament on the other hand came pretty late, and just played a very niche style that no one really was able to copy.
I question the influence of the big 4 honestly...I think a collection of underground bands was probably more influential.