I have the wired one so no battery pack there, but when you turn it around, the places behind triggers are not completely levelled with the rest of the surface (I have no idea if I'm making any sense here, it's 3:20 in the morning), unlike the Wii U Pro which also feels bigger for some reason. When I compare them directly the Pro is maybe a tiny bit bigger but definitely not as much as it feels.
And you are right, the sticks are godlike. Didn't like them at first because they were so damn sensitive but got used to them and love them now.