As for the vampires vs werewolves trope, it goes back as far as an episode of "The Real Ghostbusters" back in the 1980s, and before that there are odds and ends such as the Spanish horror films Los Monstrous del Terror/Dracula vs Frankenstein (1970) and La Noche de Walpurgis/Werewolf Shadow/Werewolf vs The Vampire Woman (1971). I suspect it's just a natural result of things to want to see two famous monsters fight. The same way Godzilla vs King Kong or Freddy vs Jason came about.
In the World of Darkness, it always struck me as the natural outgrowth of both societies. The Kindred are a perfect storm of arrogance and paranoia that only a bunch of immortals who still run the risk of violent death can be, while the Garou are a dying breed of religious crusaders with the pure zealotry that can only come with having objective proof that your beliefs are true, and both are apex predators who instinctively want to be in charge of whatever territory they're standing on at the moment.
(This doesn't even get into something like the Silent Striders, who have a historical reason for hating the undead on top of all that.)