For me, FFIII on the NES was more difficult than FF II and FF I (Origins, Normal difficulty), the Cave of Shadows was a nightmare and the final boss.... try it without ninjas or sages, I did and the battle was won purely by luck.
FF IV Chronicles version was really tough too, but if you grind enough(like I did in the final dungeon), it was a cakewalk. As a matter of fact, some bosses in the final dungeon couldn't be beat if you weren't high enough level.

EDIT: You should try FF V too, some of the bosses are really challenging.