I have thoroughly explained it many times, including in my most recent playthrough in the FF playthrough thread. (Linked
here)
The NES version isn't very difficult. It's actually pretty easy, especially with the total imbalance of ninja and sage, which were totally nerfed in the DS version.
No, I prefer it because it's faster (this applies to
everything, from field movement to battle speed), sounds better, and has more even balance (until the end, at least). It also allows more enemies on screen at once, which allows for more interesting battles, and has a much, much more consistent visual identity than the DS version. The story added in the DS version is barely anything at all, and is only applicable up until you get all of the characters together. Everything after that is completely faithful to the original. FF3's story is lighter, more akin to a Dragon Quest story (which, incidentally, is what it's going for, being a response to DQ3 and all). There are some moments in FF3 which hit me really hard, particularly the fate of one of the characters. And the moment when you transition from one world into the next is one of the most memorable moments in gaming for me, too.