I would argue that a vampire bitten by a werewolf would not change as since vampires are walking corpses; essentially a zombie inhabited by an evil spirit that needs human life to stay active in the body. The disease of lycanthropy could not affect a vampire since there are no living systems to infect.

On the other hand, if a vampire bit a werewolf, it wouldn't mean anything unless it bit it in such a way as to turn it. Then the lycanthropy would be cured leaving a normal vampire. The disease of lycanthropy couldn't affect a dead body.

(Old legends say that if a werewolf is killed, it's head has to be cut off and the body buried at a cross-roads or it will return as a vampire. The tortured body of the beast is an excellent host for the evil spirit that would inhabit a vampire.)