From a World of Darkness perspective... (Because one has to assume that this is in an alternate version of our planet, or some other planet, so my theory is going to be based on WoD because it is a structured idea of an alternate universe that I know fairly well, and includes most of the choices and would be easy to imagine how the other choices would fair in such a world)
I think I'll do this sort of how Barbeau did:
Ninjas beat Pirates:
ninjas win because they are sneaky backstabbers.
Elves beat Dwarves:
for...the same reason actually...
Vampires know better than to fight against werewolves on their own so they make a truce with the giants to take them down. The giants, too unintelligent to see what they are getting into, agree. The Vampires have the giants take the front line and attack the werewolves head on while the Vampires surround the entire area and infiltrate all of their minds causing mass confusion and leaving both sides (Weres and Giants) disoriented enough for other vampires to rush in and kill them all... because they too, are sneaky back stabbers...
Cyborgs defeat Orcs because of their advanced weaponry, but wizards beat them because of their magic.
Which leaves...
Ninjas, Elves, Vampires, and Wizards.
The ninjas realize they cannot win and commit mass seppuku.
The Vampires beat the Elves because the elves are sneaky, but Vampires are sneakier, and can obfuscate...
Then the epic battle commences: Vampires vs. Wizards (I really want to say Wizards win because they don't sparkle... but that's a different AU

)
I'm really not sure who would win. Both have magical abilities (WoD), and both can be equally as powerful. It's a tough call, but I'm going to say Vampires would win, because if they were smart enough, they could simply go into hiding and kill the wizards off slowly one by one in the darkness for decades or centuries or however long it took, because they are already dead, and therefor would not die of old age.