Only gamecube controllers can be used to play gamecube games. The Classic controller cannot be used for gamecube games.
The Classic controller can be used for all VC games. The gamecube controller can be used for Most VC games. The wiimote can be used for a limited number of VC games (i.e. games for the NES).
The classic controller only would work for a Wii game if And ONLY IF the game was specifically made to be played with it. You can't just arbitrarily switch back and forth because you don't like a games use of the Wiimote.
