From what I can feel, and no this is not scientific... GCN controller adapter in Smash 4 is slower than Wii U Pro Controllers and the Wii U Gamepad.The lag in the USB adapter is probably entirely dependent on the USB polling rate, and it probably even varies between Nintendont and other software. I remember reading tweets where, previously, Nintendont's polling rate on USB devices was 33ms (which means that the button press would lag anywhere between 0 to 33ms depending on which part of that interval you pressed the button, which would just be awful and feel incredibly inconsistent), but it was shortened to somewhere between 6ms to 10ms in a later update. My 4ms average reading for the adapter on Wii would peg the polling rate at about 8ms (4 is halfway between 0 and 8), so that checks out. Not perfect, but not something you'd notice, either.
(FYI: Dedicated controller ports, not USB, tend to have a sub-1ms polling rate.)
I'd like to check a regular Wii retail game on both Wii and Wii U (no homebrew) to see if there's an inherent difference in how the two consoles handle Wii games, but I'd have to hack up a classic controller to do it. Maybe later.
Even though it's off topic, I'd love if you were able to compare the two to see if I'm correct. I think it would be thread-worthy for all of the Smash fanatics on this board.