I would say their quality are not much different, I'm talking about early 2008 Standard (ones before the PCB mounted on the electronics).
Classic will sound hotter due to their ceramic pickups, Standard will have more vintage sound due the burstbucker pro in them.
Classic has greenish yellow inlays where Standard has regular pearl inlays.
Classic has slim tapper 60's neck profile, Standard has 2 options, 59's rounded and slim tapper 60's neck profile.
Classic will have the pick guard mounted by default, Standard will have it inside the case but not mounted (no drill holes on the body).
Which sounds better? It's subjective.