Between And Justice For All... and the Black Album they found something called mids... :D
And Justice For All... was also heavy layered, so it wasn't that the main difference IMO. I think the Black Album was when Jaymz started using the Mark IV as a preamp, so that has to make a difference too. New producer also?
You didn't say what guitar you want the tone from, and that makes a difference. I stated recently that I got a pretty close tone... with an Abraxas on an ES-333. Put the same Abraxas on a mahogany Explorer, and you will be nowhere close.
Not knowing the guitar, my vote goes also to the Miracle Man, but depending on the guitar the Cold Sweat or C-Bomb may also do good. For the neck pickup, Cold Sweat.