With a 4x4x4 cube, it's possible to apply the same strategies as for a 3x3x3, either treating it as a 3x3x3 with a double-width middle or else as a 2x2x2 and just working on the corner "quadrants". Centres of each face can also be handled as a 2x2x2 cube, ignoring the outer layers entirely.
Is it better to apply those strategies in one order rather than the other?