I voted for Metallica, and personally dislike the use of "Metallica fanboy" in this situation because the metal community has created a false stigma where "if you like Metallica, you only do so blindly because you're wrong and they're awful now," as if I'm supposed to be apologetic for liking a band. Of course it's all opinion, but even as someone who considers themself to be a Metallica fan, it doesn't mean I have to like everything they've done. St. Anger was a huge piece of shit with no redeeming quality.
Now that that's out of the way, here's the way I look at it: a lot of people think Metallica dropped off at some point, but I've heard the "breaking point" occur from "after Mustaine left" to "St Anger", which means even among the haters there are people who appreciate all of their albums up to that point. You don't have to keep liking a band when they change their sound, but you don't have to assume that they are no longer "trve" (I hate black metal fans tbh for this reason) based on YOUR personal preference. I'm of the opinion that the black album, load, reload, and death magnetic all had some massively good songwriting and structure that are still more complicated and intricate musically than a lot of other bands who pretend to be really technical.
I have a lot of respect for Slayer and Anthrax, but I can't listen to their later work because not only has their sound not changed, but the same structures and gimmicks get worse progressively. Does anyone really think Slayer ever topped Reign in Blood? Megadeth is great and I love their new work (picking up the dude from Jag Panzer was a great addition), but they've had dark periods too... I don't know anyone who is willing to sing the praises of "The World Needs A Hero". If all you care about is "who is playing the heaviest/hardest" or "who has the most hardcore lyrics", that's fine, but you're not allowing yourself the opportunity to be exposed to a rather large part of the Metal community who is still playing music.
So my gripes with that aside, the "Big Four" list is Amero-centric. The entire world has great stuff to offer from all corners, including some Metal pioneers of their own. S.A. has Sepultura, Sweeden has Dark Tranquillity and In Flames (A band who is much more deserving of the Metallica-esque criticism of 'used to be good, completely changed their sound and removed all musicianship from it'), Switzerland has Eluveitie, etc. Each genre has their own roots that have been hailed and replicated - even the big 4 rest on the shoulders of Sabbath, Zeppelin, Deep Purple, Iron Maiden, Dio, etc - largely non-American bands. The idea of "the big 4" in general was always a marketing technique aimed at getting the top 4 selling American artists to play together and nothing more. Don't get me wrong - I'm a huge fan of all 4 bands (and own the entire discography for 3 of them), but to make a list of "most influential/best/whatever" Metal bands in general is a huge waste of time based on the diversity and size of the genre (without even going into the subjective nature of opinions).
/rant