It all really depends on the preferences of the player and just what kind of story you're looking for. The way I see it, each Final Fantasy game, while having recurring similarities, have different kinds of stories they are trying to tell. Some may belong in the same genre of story but with a different spin to it.
In fact, a lot of my favorite FF games, while they are my favorite, I will admit are not the best kinds of stories compared to other FF games
of the same genre.
For instance, FFX (my favorite FF game) is a good "fish-out-of-water/guy-ends-up-in-a-new-world" kind of story, but I think Final Fantasy Tactics Advance did it better in terms of story (minus the romance).
I absolutely hate FFXII but I will admit that while their characters (except for Balthier) are poor for FF standards, the story did a FANTASTIC job in creating a lot of riveting political drama, leaning away from melodrama and going for a "war of nations" story. Also, the theme of a "ragtag group of fighters that are only connected by a common goal" is done A TON more well than FFXIII, which I also liked but believe that the characters would have killed each other sooner than realizing they should work together.
Now I know many people consider FFVI to be their favorite and I can see why (I liked it a lot), but I have to say that the storyline is actually VERY basic and simple. What makes it good is the characters. However, what makes the "story" good is to keep the players guessing what to do next alongside said good characters. Unfortunately, FFVI, at least to me, was VERY predictable (
except for the last third of the game. You know what I'm talking about). Not bad, but in this day and age, I've seen it done before.
Also, what makes a storyline really good is stuff that could be considered "optional" in terms of the main plot. Such plotlines give the story depth and allow you flesh out not only the characters, but also the world the story takes place in. Both FFVI and FFVII do this exceptionally well with many character driven stories that involve interacting with MANY places in the world. A special mention to FFVII for, while they are sometimes mediocre, created additional games to continue and/or expand the universe (i.e. Crisis Core).
Again, it all depends on the kind of story
you, the player, are looking for. Everyone will have different opinions and will undoubtedly defend their "favorite/best Final Fantasy game" to their graves. To say one has the
"best storyline" is impossible to answer as each game is different and not meant to be intentionally better or worse than its predecessors or future installments. They are made how the creators made them: on their own standing using what they have learned from their experiences/games and with the intention of telling the story they want to make.
...well crap, now that I've said all that, I can't pick which storyline I like the best