Well it would also depend on how old they were because usually the older the beast the stronger, because of their knowledge and experience. But if they were both the same age then I would say the Balrog would win. He would not be affected by the Dragons fire and the Balrog would use his flame sword and stab it into the Dragons underbelly which is very soft and is the weakness of a Dragon. A Balrog is a Maiar and he could defeat the Dragon, because I do not believe that Dragons are Maiar. The Balrog might be able to trick the Dragon because He has the power over both shadow and flame. They are both however very smart creachers. But in the end I believe that the Balrog would be the winner in the end.
