To preempt any pedantry, I’ll correct myself:
Of the three named inhabitants of Arda - two of which were Children of Iluvatar- that are known to have slain a Balrog, two were High Elves and the other was Gandalf the Grey. None of these “survived” the encounter, either.
It’s highly likely that Thorondor, Lord of the Eagles, killed dragons during the War of Wrath, as he and his fellows were with Earendil at the end.
I can’t think of any other named beings. Anyone?
Balrog over Smaug.
But not so certain that would hold true for Ancalagon the Black. Ancalagon took on the Host of the West, Vala included, and was not conquered until Eärendil in Vingilot and Thorondor took him on. When he fell, he broke three peaks in his death agony. Yeah, that’s pretty chill.
They are both fire immune, Smaug is also immune to weapons anywhere except on his belly and has mind control. Balrog has no chance at all unless Smaug is dumb and flies around.
The dragon might be immune-ish to arrows, but so what? The balrog, immune to the dragon’s fiercest weapon, might instead mere grapple with the dragon and finish him with, say, strangulation or blows. The balrog also has magic at its beck, so it has most of the cards. It would be a wrestling match to behold. WMEWL.
I think it depends on the contest. Dragons are clever and cunning, so in a game of, say, chess, I’d give the edge to Smaug.
But balrogs are badass and nimble. In a game of, say, basketball, I’d give the edge to the balrog.
I believe the literature supports my position:
Which is exactly what he is/did when he got killed. Smaug is dumb. Bilbo even called him an “old fool”.
I think he would be less likely to underestimate a Balrog than a buncha midgets though.
Isn’t there some nerd-game out there that has already modeled both smaug and a balrog and can put them in a thunderdome?
A Balrog is a Miair A primordial being, like Gandalf or Saruman or Radagast or Sauron.
Smaug is simply a created lesser being made by Morgoth.
And of course he can not actually create life, just bastardize what is there.
Some of you say that even Gandalf would not take on Smaug.
I disagree, it is not a case of could not, it is a case of not allowed.
Gandalf has great limitations on what he is allowed to do, he is more powerful than he ever displays.
He must work with in the confines as dictated by Eru
(Frustrating Job being Gandalf)
Gandalf simply may not directly confront Smaug, he can not, doing so will be meaningless, just as matching Sauron power for power would be.
Middle earth is changing, the time of elves and magic is over, and the time of men is beginning, the reliance can not be on magic.
Anyways i am babbling
Balrog is a fallen Miair, i don’t think he has to follow the restrictions Gandalf does, he already does not care about what Eru thinks, so should be capable of dealing with Smaug.
Adding
Smaug is not all that either.
His armor is not indestructible,
No mans sword or spear or arrow might piece it, or so he says, but that has nothing to do with a strong being ripping the armor off him.
The black arrow knocked a scale off, a strong being could rip scales off him.
Smaug vs Gothmog?
Well Smaug can forget his fire, that’s like giving Gothmog a nice bath.
Wings? yea not so much, dont think a small hurricane bothers a balrog terribly much.
So all he has left is tooth and claw.
And Smaug is not very intelligent, he is easily antagonized, easily outwitted, easily drawn into a compromising situation
And mind control, which is how the author of the article in the OP had him winning.
Balrog is a Miair, not a man
Unless the dragon flies away, the Balrog wins by ripping Smaug’s legs from their sockets and smacking him in the head with his own claws, repeating “why are you hitting yourself?” until Smaug dies of shame.
What if they fought on a treadmill? And a pissed off Teddy Roosevelt shows up?
Uh, no.
No knock offs. 
You can kill a Balrog with a spear made from the wood of a Sapient Pearwood tree that grows in Far Harad. It’s a fact look it up.
The Balrog IS fire. Or maybe more like lava. He is a fire demon, so yeah, Smaug can’t cook him.
The only other killing method Smaug has is to pick up his victim, and drop him from a height. The Balrog survived a fall to the center of Earth (or thereabouts) and continued fighting Gandolf. So that’s no good either.
Smaug also has his armor of in-grown treasure. In this case, it’s really just going to make him tire faster.
Balrog has his fire whip, so my take is this: as soon as Smaug gets close enough, Balrog lassos him with the fire whip, and then just hugs him close and holds on. Eventually, Smaug’s armour will melt, and he’ll slowly cook.
A bit like the death of “the Dragon” Viserys in ASoIaF. Or maybe more like that Moroccan fish dish where they bury the fish in salt -head and all- and stuff it in the oven for a couple of hours.
Anyway, that’s how I see it coming out . . .
Yes, but the spear has to want to kill the Balrog.
That used to be someone’s signature here, wasn’t it?
But that’s exactly how Gandalf killed his Balrog:
“I threw down my enemy, and he fell from the high place and broke the mountain-side where he smote it in his ruin.”
Don’t tell me Gandalf can throw a Balrog farther than old “hurricane wings” Smaug.