I think this is a better wildranger question, what genre of metal is the most popular? I actually think it could be thrash but maybe classic metal. I'm not really sure.
Which big trio is more popular: Black Sabbath, Judas Priest and Iron Maiden (classic metal) vs. Metallica, Megadeth and Slayer (thrash)?
Of those six bands, Metallica is the probably biggest, but all three of the first trio are probably bigger than Megadeth and Slayer.
I think the question is whether the combo of Sabbath, Priest and Maiden is more or less "popular" than the combo of Metallica, Megadeth and Slayer.
I'm not sure how that could possibly me measured in any meaningful way, but I think that, although Metallica is arguably the most popular of the six bands mentioned, the "classic metal" combo is "more popular" than the thrash combo.
The Big Four of traditional metal? Short of a one-off festival like a Live Aid or a Cal Jam, between Purple, Sabbath, Maiden and Priest, who's the opener on that show? All four have or do tour stadia, all four are in or are in consideration for the RnRHoF, all four have at least one album that is a classic OUTSIDE their genre... all four have a song that has trancended even the more general "metal" or "hard rock" boundaries. Even your girlfriend knows Paranoid, Smoke and Living After Midnight. I'm thinking she might not be all that up on "Antisocial" or "Symphony of Destruction" or "Raining Blood".
I'm a bit more of a thrash fan than you, but I certainly don't go deep and far prefer "classic metal" bands. I love Metallica up through AJFA and tolerate the Black Album. I love a couple Anthrax albums (Spreading the Disease and Among the Living), but you're right that they never moved beyond the "minor leagues." I hate Megadeth and only like a couple Slayer songs (musically, but not vocally). That said...
The opener of a Purple/Sabbath/Maiden/Priest is unquestionably either Maiden or Priest. How to decide between the two I don't know; nor do I know which of Purple or Sabbath would headline.
Also, I'm wondering which Maiden and Priest albums are "classic OUTSIDE their genre" and which Maiden and Priest songs have "transcended . . . the more general 'metal' or 'hard rock' boundaries." I hear Maiden songs fairly frequently at hockey games, but they're there precisely because they're metal songs and hard hitting (played for the same reason that they play Seek and Destroy). Priest had a song in a car commercial a few years ago, but again, it was there precisely because it was a metal song.
My wife probably knows Paranoid (although not likely by name), but I seriously doubt she knows Living After Midnight. She might know Breaking the Law and definitely knows at least half a dozen Metallica songs by name (and maybe a few others not by name). If LAM is your example of a Priest song that transcended metal boundaries, maybe it did so 35+ years ago, but I'd lay good money that, with the possible exception of two guys who are in their 40s, none of the 15 or so people in my office are familiar with that song. I also think Peace Sells is at least as "transcendent" as any Maiden song.