Oh yeah, they did remove the rotating building, now you just kind of wait for the door to appear.
I think the charm people say isn't captured in the remake is just nostalgia getting in the way, the gba version is almost identical when it comes to level design, and the updated visuals and audio look fantastic on the gba.
That isn't to say your wii points shouldn't be spent on the original, as already stated the game really pushes the nes hardware, the only downside is it suffers from frequent slowdown.