More like several fanbases as opposed to two. You have people who like the new games exclusively, people who like the old games exclusively, people who like the new and old with some exceptions (basically most of SonicGAF), people who just like the comics/SatAM stuff, and 'that' segment of the fanbase which should be ignored outright and rightfully so.
FF's fanbase has a similar sort of split, and a similar set of fanbases, but it sometimes feels like the bases split more often because every game is divisive. There's all sorts of media out there for people to engage in like anime, light novels, and Advent Children in order to get introduced to the FF series. So going back to your example, people aren't really discussing the same thing when they want to talk FF because the FF media (whether it's anime, novels, movies, or games which create dichotomies of their own) are so different. People look for different things in FF.
From my perspective, FF isn't exactly what I want it to be at the moment, and I don't have a large appreciation for the current FF13 trilogy or whatever it's supposed to be. I'm not looking for stuff to look badass in a cutscene, nor do I desire to watch a ton of cutscenes. I just want a nice battle system, quest diversity, cohesive design, and maybe compelling characters on the side if I feel like the story and characters are written well. The FF13 games haven't done much for me in several of those aspects.
I can go back and play older FF games and enjoy my time with them, and I can get into newer RPGs in general. Thus my assumption is that I haven't grown out of the genre at all, but rather, it's just this set of FNC games that I don't find particularly engaging in most aspects (ex: story, characters, quests, etc); hence my desire to move on from the world. I'll still play the new game because I want to see if they've made changes or improved on systems, but I don't know if I'm going to like it from an 'overall package' standpoint.
I don't see it as a bad thing that people like the FF13 games, really; even if I snark about it. People like what they like, and given how FFXIII-2 ended, there should be a sequel explaining the consequences of the ending. Different strokes. I'm sure there'll be a future entry that I'll enjoy as much as how people who like the FF13 games enjoy them.
Edit: hey. At least the FF13 games aren't anything like
this giant pile of garbage.