As has been stated, less drag and weight. Unfortunately there are disadvantages - trying to combine both rudder and elevator functions can be difficult and there is more stress on the tail section when the aircraft experiences yaw and pitch.
Looks good in my opinion though. I always thought that the old V-tailed Bonanzas were among the nicest-looking GA aircraft.
Twin tails on the other hand, a la F-14, F-22, SU-27 etc. can allow bigger rudder area and also reduces the aircraft's weight. Also if you get one tail shot off, you still have another one to help get you home
Smithy