The one for the original LoZ remixes the dungeons and places them in different areas of the overworld. The overworld stays the same, except some caves are in different places etc. It's much harder.
I just beat AoL today, so before now I didn't even know it had a second quest. This one isn't really anything special, the same game just starts over, but your spells, sword skills, and stats are carried over from your first quest so you can use them from the get-go. This actually makes the second quest surprisingly easier than the first, or at least it gives it a decent difficulty curve. I beat the first four dungeons of AoL's 2nd quest in an hour without even getting a game over screen.