Queensryche, by a mile. I love Metallica's early stuff, but they fell off a cliff for me, stylistically, with Load and moving forward. Queensryche did the same, as the original lineup stuff was all gold up UNTIL HITNF, and then that was a little spotty to say the least. But I think QR's post-DeGarmo catalog is way better as a whole (again, for me, personally) in comparison to Metallica's post-Black album catalog. So this one is an easy one.
The one advantage I do think I'd give to Metallica is that they have three all-time classic records (Puppets, Justice, Black album), whereas Queensryche arguably has only two (Mindcrime and Empire). And again "classic," is subjective. For example, I think Promised Land is one of the band's best albums, but not everyone agrees.
So, Queensryche, by a mile.