What Final Fantasy III's story does do better than Final Fantasy II, is that it has stronger themes to it. The background of the story is about restoring the balance of the crystals, the villain Xande is a much more fleshed out antagonist than his forebearers due to having a more sympathetic story about fearing his new found mortality. The final stretch of the game involves the party battling an eldritch being of unfathomable power despite already losing once to the beast and the hope needed to make the impossible possible. If you don't believe me when I say these themes are intentional than I would say you've never seen this game's ending as the closing narration pretty much point blank explains to you the themes of the game. Whiel Final Fantasy III may not have the space or technical muster to display these themes in a more artistic way as it's future installments will do, it doesn't change the fact that Final Fantasy III's themes will leave the player with something to think about after it's all said and done. In that way do I feel Final Fantasy III does stand as one of the better stories in the series.
THANK YOU. Finally someone else but me to realise that FF II was not, in fact, the best FF story-wise on the NES and that III is not that game that "returns to gameplay over story like in FF I".

III was hands down the best entry on the NES, period. It was the best in every category. Graphics-wise, sound-wise, music-wise, story-wise, gameplay-wise and technical-wise. Everything FF I and II did, and without taking away of the importance of those two games, III did better. III is life. III is god. All hail Final Fantasy III as your lord and savior!

As far as remakes go, is it bad that I think that XIV was a better remake of III than the DS version? ^^"