I think some of you are missing the point of the big four, the big four is made up of Thrash Metal bands, some of your favorites may not be on the list because they arn't Thrash, for example, Iron Maiden is not Thrash, Death is not Thrash, I enjoy both bands but not the right catagory.
Anthrax never sold out like Metallica, weren't too full of themselves like Megadeth, tried new and interesting things unlike Slayer. So I think I respect them the most, even if their music wasn't always best in class.
Though, if you try going back to Spreading the Disease it sounds really fucking dated where if you go back to Metallica's first 4 albums they still sound fresh and still haven't been outdone.
I'm not a huge fan of Anthrax but if you haven't heard their newest album I'd give it a listen, really good shit.