[lathspell]

I think that if we take Balrogs & Dragons in general, as would be the most succesful in this kind of discussion, and leave out the worst, baddest and nastiest of both kinds, than both of them should be thought of as extremely strong.
Though the Balrogs had magic, and very strong magic, the Dragons were undaunted by it. Balrogs had whips and swords, dragons had teeth, claws and a very strong tail. I think the greater Terror would come from a Balrog, though there would still be a great deal of fear coming from a dragon.
We do know more dragons and Balrogs, but let's take Smaug and the Moria-Balrog. I think that if they would fight together, the Balrog would loose, but when they both had to fight mortal men or elves, the Balrog would do the greater damage, because weapons are no harm to him as Gandalf points out: 'Go. Weapons are of no use here' and 'This is foe beyond any of you' (even Aragorn)...
So I don't think it would be a matter of 'who is strongest', for there is no way to find out such a thing. I think it depends on what you are fighting in what area and what his skills are.

btw: I think a Dragon would have more succes against Gandalf than a Balrog.

greetings,
lathspell