The disease you contrast first should dominate. Hybrids are cool, but come'on...we're lucky enough if both vampires and werewolves make it in at all.
If I remember rightly in Bloodmoon, whichever one you had contracted first, or if you were already one of the damned, it would cancel the other out.
There was some sort of message saying Porphyric haemophillia ousts the lycanthropy in your system or whatever, It's been so long since I've played it I can't remember.
I doubt both diseases would work in a synergy of sorts, I could see one digesting the other in it's bid to consuming your body, besides, the Vampire of skyrim are a different clan of vampires aren't they? Don't they reside underneath frozen lakes waiting for their victims to walk over it so they can pull them under without breaking the ice?