Well, the Black album is what made them one of the greatest bands in the history of rock. It is the most commercially successful album in heavy metal. It made them mainstream with Enter Sandman, The Unforgiven, and namely Nothing Else Matters. Does not mean it is their "best" so to speak. It's just the album that the average music listener will know. My favorite song on the album is My Friend of Misery. Love the intro bass line.
Master of Puppets, among hardcore Metallica fans, is considered their masterpiece. Which it is. However, in 1986 Metallica was not known commercially and were just starting to crack the surface then opening up for Ozzy Osbourne and rocking the crowds harder than he ever could. The average music listener isn't going to really know this. But it's got some of their greatest songs on it. Battery, MOP, Sanitarium, Disposable Heroes, Leper Messiah, Orion...this is the archetype for any heavy metal/thrash metal band, in my opinion.