We have a fairly specific idea of what vampires and werewolves are in our society. Vampires are cursed with the need to drink blood and immortality, werewolves are cursed with changing into a huge man-wolf during the full moon.
Recalling Sauron's shape-shifting showdown with Lúthien and Huan in the Silmarillion, this does not seem to match up.
[Sauron] took it upon himself the form of a werewolf, and made himself mightiest that had yet walked the world; and he came forth to win the passage of the bridge.
and when Huan released him
... immediately he took the form of a vampire, great as a dark cloud across the moon, and fled dripping blood from his throat upon the trees, and came to Taur-nu-Fuin, and dwelt there, filling it with horror.
I suppose (and seem to recall) that a werewolf might just be an evil spirit in the form of a giant wolf, but what on earth (Arda?) would a vampire be in this context? This is assuming that it would not be somehow beneficial for the already immortal Sauron to have a mandatory diet of blood. ;)