I think the feud between the two is more of a new idea.
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The myth of werewolves dates all the way back to ancient Greece. King Lycaaon was transformed into a wolf after being cursed by Zeus. He was given the name lycanthropos (λυκάνθρωπος) from the words "lukos" (λύκος) meaning wolf, and "anthrōpos" (άνθρωπος) meaning man. According to the myth a man could find himself transformed into a lycanthrope by either being cursed or bitten/scratched by another. There were several other wolf-men in Greek myth. The Neuri were believed to be a tribe of wolf-men who transformed once every year for several day at a time then were changed back. Ovid writes of the Arcadian wolves in
Metamorphosis. Werewolves are most often associated with European lore, but it was first found in Greek myth (King Lycaaon predates the flood myth that ended mankind and brought about the Age of Heroes or Iron Age). Lycanthropes can also be found in Native American myth as well as Midieval lore. Lycanthropos were believed to have appeared in Greek myth before 200BC.
The connection between werewolves and vampires in European legends can be found in similarities between the two monsters. Both can be killed by decapitation and silver bullets (also stakes to the heart and sunlight for vampires). Both thrive during moonlight hours. Both are created via bite (also scratch for werewolves).
In Midieval Europe there were cases of lycanthropy that actually led to trials and executions. The corpses of those "werewolves" were burned rather than buried to avoid the corpses returning to life as vampires. Ancient Greeks also believed that if the corpses of wolves were not burned, they would later return as blood-drinking hyenas. These vampiric werewolves would return to their human form at daylight. After they were discovered they would either be decapitated with a spade or exorcised by the parish priest. The head would then be thrown into a stream, where the weight of its sins were thought to weigh it down. Sometimes, the same methods used to dispose of ordinary vampires could be used. The vampire was also linked to the werewolf in East European countries, particularly Bulgaria, Serbia and Slovenia. In Serbia, the werewolf and vampire were thought to be one creature known as the Vulkodlak. In Hungarian and Balkan mythology it was thought that a vampiric witch could become a wolf to suck the blood of men born under the full moon in order to preserve their health. In their human form, these werewolves were said to have pale, sunken faces, hollow eyes, swollen lips and flabby arms. The Haitian jé-rouges differ from traditional European werewolves by their habit of actively trying to spread their lycanthropic condition to others, much like vampires.
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I think it's just easy to see the two and wonder what would happen if we stuck them together in a cage match, who would win? It was such a good question that everyone decided to make it into their own idea. They wanted to draw out their own fight and decide for themselves who would win. I guess it's like Mortal Kombat and DC Universe. Great fighters from two different worlds-lets see what happens. It was obviously a good idea because it's really caught on. But I've never come across an originial Vampire vs Werewolf legend.