Although it's still not an arcade-perfect port, Donkey Kong: Original Edition reinstates a few of the things that the original NES release was missing. The most significant of these is that the second stage, with conveyor belts transporting cement, is now accounted for once again. It's arguably the most annoying out of the four stages, but it was always a bit silly that such a short game somehow lost an entire stage in the transition to home consoles; it's good to see it back.
A few other less important things have also returned, such as the animation of Donkey Kong grabbing Pauline and climbing up to the next stage every time you reach the top; inexplicably, though, the iconic screen in-between stages with multiple Donkey Kongs stacked on top of each other that shows what level you're on is still missing in action.
Since this is basically the original NES release of Donkey Kong with some additions, it means that the NES-exclusive features are also still available you can still opt to play a secondary game mode in which the game gets harder much faster, as well as a two player mode where, if you link up with another 3DS, you can take turns tackling stages.