If Eorzea and Vana'diel are the same places at different time periods, I would think that Eorzea is far in Vana'diels past. Primarily owing to the lack of crags and other similar Zilart structures. There are other things you can look at to draw this conclusion. The ant mobs look like devolved Antica. The northern areas (North shore of Batallia, Sauromugue, and Qufim island) all have a blackened, crystallized look to them, as if some giant magical explosion occurred in the northern region. We don't see that anywhere in Eorzea. (I always wanted to know what caused this...) But if they're happening on the same planet, they're obviously continents that are so far apart that they have no contact with each-other. So much so that the guardian Avatars of Vana'diel are instead vicious Primals in Eorzea. No, I think they might have some kind of relationship, but they're not the same world, past or future.