The only difference is the box/packaging, which is the EU version/graphics. However, as noted above, the actual controller itself is 100% identical (model number, manufacturing specs, etc.) to the original controller that comes with the NES Classic. Seeing as how the US packaged version of the controller is extremely hard to find (and expensive!!!) this is the best deal you can find.
I received the official Nintendo controller and can verify it is identical to the one that comes in the original box included with the NES Classic. This means it functions and plays exactly the same – with a fantastic d-pad and tactile, responsive A & B buttons. Unfortunately, this also means it has the same short cord length (2.5ft) but this can be rectified with 3rd party extension cables.