Metallica, Megadeth, Slayer, or Anthrax.
Metallica has some the most complex music of the four (and most commercially succesful). Many of their songs are consider top contenders for greatest metal songs of all time. However many feel that Metallica sold out for profit with the Black Album and even more so with "Load" and "Reload". And worse yet they were accused of losing touch with the fans completely with "St. Anger". But "Death Magnetic" has been hailed as the "Great Comeback Album" for Metallica.
Megadeth has one of the most unique sounds of the four, both with vocals and instrumentation. They like Metallica stayed thrash for several albums but then diverge to a more radio freindly old school heavy metal sound which included the much disliked album "Risk", they too eventually floated back to their Thrash roots first with "The World Needs a Hero" continueing onward into "Endgame" which is their most recent album.
Slayer is noted for three things above all others. One, they are the fastest of the big four. Two, they parted ways thrash less than the other three.ANd finally the perceived Satanism stand. (which is not true, they are not satanists,) They are also noted for their controvesial lyrics about serial killers and nazis. However one things stands out that can't be argued with, while megadeth and metallica sometimes gets close, the other three can not beat the blistering speed of Slayer. "Reign in Blood" is considered by many to be the greatest of all thrash metal albums (which i personally agree). However Slayer has been accused by some music critics of having a limited range of musical expression and unable to succesfully create a different sound other than the dark Thrash metal.
Finally Anthrax, my least favorite of them. Anthrax is a good band, however they are the least succesful of the four. I haven't as much to say because i don't know as much cause i'm not as big of a fan. However Anthrax is the only one of the "big four" to change lead vocalist, they are also noted for their foray in "Rap Metal". They do have a very unique sound that has contributed to their success over the years and even though not being a fan i'm glad to know that the band did not break up as it was orginally suggested that they would. To lose on of the Big Four would be a terrible loss in the music industry.
Pretty much this about what you think. I tried my best to express what each band was about and what stands out. Ultimately you be the judge. Who is best, Metallica? Megadeth? Slayer? Anthrax?
Here is my list. 1. Metallica 2. Slayer (only just barely do i prefer Metallica over slayer and only because of the beauty that is in some of Metallica's songs) 3. Megadeth 4. Anthrax.