It's a bit sad if fans regard the aesthetical elements, such as airships and chocobos, to be the only things that comprise Final Fantasy "lore".
To me, those have always just been the building blocks of a franchise; the rules set and templates that are used to create a much larger game.
In a more tongue-in-cheek fashion, I think GoGoStarsfall hits closer to the mark, regarding Final Fantasy lore. The stories typically follow this pattern:
the Bad Guy is not the REAL Bad Guy. Fake Bad Guy dies and then Real Bad Guy, who is a demon destroys you're family, then the world! (this is fun lol :P)
It's a very familiar storyline that is present in a great deal of anime and manga, which is probably where a lot of the story inspirations come from originally, and is also, to me, a great part of Final Fantasy's lasting appeal. It offers a different approach to storytelling that I don't usually get from Western RPGs, which are typically make sharper distinctions between good and evil.
Most of my favourite Final Fantasies eschew the simplistic moral divide that pervades so much of Western, Christian-inspired fantasy and RPGs. Final Fantasy villains (except for the odd few like FFVI's Kefka, who was the very definition of "chaotic evil", and FFVIII's Sorceress), while typically megalomaniacs, tend also to have greyer, more human motivations. Also, in typically Japanese fashion, the ultimate evil facing most of Final Fantasy's heroes is not some demon-inspired Armageddon, but rather usually some deluded attempt to take all life and reality to a higher, evolved plane of existence (which was the case in FFIX, for example, and very definitely for the Zilart in FFXI).
All the above, to me, is what truly makes Final Fantasy "unique" in the JRPG genre. All the other major franchises in JRPG have their own distinctive features as well.