Actually the story mode are always consistent in the game manual books
(except the Game Gear and SMS version of course since they were based on the anime version).
Manga, colab games, and anime version are the ones who took different approach of the stories but the canon one is the one in game manual books.
Yeah but that's just it, the overall story is mostly just a blurb in the manual.
In games like Mortal Kombat, Street Fighter, Tekken, Dead or Alive or SoulCalibur, these games have campaign modes where you can be involved in the story than just read about it.
It would be nice if the Virtua Fighter series has more of a fleshed out story. If it did, I'd believe it would be up there with DoA and Tekken.