I don't know if you watched the same trailers as I did, but XIII and Versus XIII don't look like they are related at all, nor are they related to any of the previous FF games. I think people should have figured out by now that the number at the end of the FF simply shows only the order in which the games are made. Naturally it wouldn't make any sense to call one FFXIII and one FFXIV when they're being made at the same time. The "versus" just indicates that there is some competition between the two games to see which team can make the better game. I think that is a really innovative approach on Square-Enix's part.
Of course you can't really judge a game by its trailer, but from what I've seen, XIII looks like it will be more graphically stunning with a flashy cinematic feel, and Versus will have a deeper story with more focus on the characters, kind of like a book. Personally, I think Versus is far more interesting as it takes place in a modern world, and it is about time someone made a good rpg in a modern setting (that's not to say it hasn't been done.)