In terms of storyline, I think FFIV is the better game. While FFIII has cool and likable characters (Princess Sara in NES, Refia in DS ^^), I still think FFIV has better character development and a better villain. Gameplay-wise, I think FFIII wins because of its job system. Both games have interesting fantasy worlds with lots of old-school elements. While both games are good, I still prefer FFIV to FFIII.
When is it said that Luneth, Arc, Refia and Ingus (or the NES characters) are 17 years old? I was always wondering how old they are, but I could never find out the answer.
Now that you mentioned it, it's a bit funny, really. I mean, FFs II, VI, VIII and X are all FF games that I don't like as much as some of the other FFs. FFVII and FFIX seem story-driven while FFXII seems gameplay-driven, though, so I don't think the even numbered FFs always have focus on the storyline.