My favorite aspects of the Final Fantasy games are characters, world building, and story, pretty much in that order. When I sit down to play a new FF, or come back to revisit an old one, these are the things I am looking for, and hoping to sink into. Of course, not every FF game has these in equal measure: the lack of world building in FFXIII kept me from investing as much as I would have liked, for example, and the stories vary in quality quite a bit, and even the games I love most (FFX, X-2, XII, and IV) have a dud character or a flat plot point here and there. But overall, I would say these have been the series' strengths for me.
As I mentioned in my answer to lassarina's question about RPG gameplay, I haven't actually played that many RPGs outside the Final Fantasy series, but the one other series I have invested in, namely Dragon Age, succeeds in all three areas listed above. Excellent NPCs across the board, interesting stories mostly told well, and a fascinating setting in the world of Thedas. So no wonder I've been drawn to it, both as a player and as a fan. Mass Effect is also pretty strong in these respects, especially the storytelling, but I didn't connect as strongly to the characters or the setting as I did to Dragon Age, or my main Final Fantasy fandoms (Spira and Ivalice). (I'm still not really sure why that was. Probably that's another post for another day.)
I think it's pretty safe to say that, so far, I've found the Dragon Age games more compelling across the board, in all three of these areas, than any of the most recent Final Fantasy titles (FFXIII and its sequel). And although I have some hope for FFXV, for various reasons I don't trust Square Enix as much as I used to -- especially not in how they handle characters and character development. It'll be interesting to see if I continue to be a fan of the franchise going forward.
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