For most classical music, you have to also need to think about who is playing the piece as well as the composer. In that regard it is similar to jazz.
A great performer can turn any piece into a work of art, but if you go and buy a classical "greatest hits" grab-bag at a Virgin Megastore, its like the music is entirely different. My dad recently bought an LP box set of Beethoven sonatas by Claudio Arrau that really brings the music to life. Very haunting stuff.
Glenn Gould recorded the Goldberg Variations twice. I believe conaisseurs swear by the early (1956) version. I do like it, but I'm certainly no judge of classical.