Nintendo should teach their 3rd party supporters their file compression secrets.

[Barozi]

As most already said, there is no magic.

video cutscenes take far more space than in-engine cutscenes (especially when they're in higher resolution)
Spoken dialogue needs lots of space.
Better audio quality needs more space. (AC3->DTS->DTS-HD->DTS-X)
PS4/X1 games have several language tracks included. Combined with better audio quality this adds up quite a lot.
Higher resolution textures