Ding Ding Ding. Its the battle of the centuries. Vampires against Werewolves.
In most fiction, these two opposite paranormal groups are bitter enemies and hate each other. Where the animosity stems from can be debated. So, lets debate
Some authors go for this simple version of things. Werewolves (especially the more mystical wolf appearance kind) tend to view themselves as a naturally occurring phenomenon along side the normal human evolution. They live, love, breed and die the same as humans, they just have this extra side to them putting them more in touch with nature. Fair enough. Then along come vampires. Creatures that are un-dead, who have had their human life and because of some virus/curse live on after death preying on humans to keep surviving. Making it a fight for survival.
An Ancient Feud
There are others that look at the relationship between the two as they could get along if they wanted to but they just don't want to. There is bad blood between the two groups stemming from something that happened a long time ago and each new generation is taught to hold the same grudge. This has been anything from two brothers, one who became a vampire and one who became a werewolf falling out over some girl (and its always over some girl isn't it) or once upon a time vampire used werewolves as slaves. This version of events allows the writers to use things like peace agreements and unusual alliances to add drama to a story.
Who would Win?
Now that is entirely dependent on what you read and choose to believe. In most I've come across, ultimately it tends to favour the werewolf coming out on top. You have numerous novels where all the werewolf has to do is bite a vampire and its a death sentence. Of course you also get the novels where a werewolf bites a vampire and all you get is one pissed off vampire with a bit of his arm missing. I have noticed though that Vampires tend to go for neck snapping quite often where as werewolves will attempt to rend their opponents, possibly for the fun of making them a canine chew toy. Either way its always thrilling to watch.