In Pokémon Rumble U, players can collect and battle up to 649 different Pokémon by picking up capsules in the game's various story arenas. Power levels seem to be determined by the level they're captured on, and skills are predetermined.
The physical figures, on the other hand, can be modified extensively. Using coins earned in the game, which would otherwise just sit there, doing nothing, players with physical toys can swap out powers, raise levels and change special traits. Stats are saved to each toy, so if I were to bring my Lucario to a friend's house, he'd still be a super-powered badass.
So I have seven Pokémon I am invested in (in more ways than one), and another hundred and change I could care less about.
Nintendo calls them optional, but the NFC figures add a level of depth and engagement to an otherwise shallow experience. If you're planning on playing Pokémon Rumble U, they are essential.