The argument for the 3x3x3 version hinges on the fact that the central cube will have 6 newly cut faces, and therefore will require 6 slices to form, regardless of rearrangement. For the 4x4x4 cube, there are 8 inner cubes, each of which need 6 slices directly acting on them. This can be done as long as the first cut in each direction is the middle one, and then the two halves can be lined up to simultaneously perform the other cuts in that direction. So perhaps counter-intuitively, a 4x4x4 cube also only needs 6 slices.