Gandalf is the same kind of being as the balrog. He is not a human, as such.
I have the impression, though, that Gandalf “threw down” the balrog only after it was severely injured in the fight from Gandalf’s sword. But I admit I might be conflating stuff from the movie.
Anyway, my money’s on the balrog.
Gandalf’s sword? When did Gandalf have a sword?
He found it around the middle of the Hobbit, and had it on him ever since.
Both Balrog and Smaug have AT Pl/20, so that’s a tossup, as are speed and size. Smaug is Level 66, while the Balrog is only 33 for physical attacks (66 for spells).
Smaug has the edge on hits - 636 to the Balrog’s 420.
Balrog has the better DB, though - 90 to the dragon’s 75
Smaug has many more attacks, though (125HBi/130HCl/150HBa/95HHo/120FBr/spells) but the Balrog’s are way more powerful individually (275wh&th/325pa&ro/spells) - I think this one will go down to the table rolls, especially crits, but it looks like the Balrog has the advantage, going in.
Having said that, I think it’s fair to say you never can tell about these things - I mean, Sauron himself once lost a fight to a dog…
Great. Now I’m going to have nightmares about goddamn Rolemaster tables.
The stats are MERP, not [del]ROLL[/del]Rolemaster, but close enough 
“Stumble over an unseen imaginary deceased turtle. You are very confused. Stunned 3 rounds.”
“You freeze your foe into a solid statue. You have half a turn remaining. Push him over, you know you want to!”
“Your target is turned into a pile of goo. Get a mop”
But of course head and all, the cheeks are supposed to be a delicacy (they’re the same as the rest of the fish, but if my mother hears me say that she’ll cook me a la sal too).
Which of each of them’s attacks would actually have an effect on the other? Maybe it’s a failure of my imagination, but I have less of a problem picturing the Balrog grabbing the big fat lizard and pulling him apart than the lizard doing something that Bally finds more painful than irritating.
Glamdring, the foe hammer.
Mine
Ultimately, whatever other advantages Smaug might have must be balanced against how strong the EPA is at the time.
It’s a Maia, plural Maiar.
Sorry.
OK, not really sorry. The fact that I can pick nits like that here is basically why I post.
Regarding the question, I’m leaning towards the Balrog, but I don’t think Smaug is right out. I don’t think we really have enough info though; what did take the chunk out of Smaug’s armour? What exactly does it take to kill a Balrog?
In Middle Earth, catalytic converters use mithril instead of platinum.
Nothing took a chunk out of his armor. He simply hadn’t managed to coat the breast near the left armpit with treasure from lying on it, leaving it bare skin (presumably the iron scales mentioned by Smaug are limited to the back and extremities, and the belly is protected by the gems he lies on).
I’m pretty sure that Smaug’s belly has tough armored scales, too. Just not quite tough enough to stop an arrow.
No, it doesn’t:
To clarify, the [DEL]fireproofness[/DEL] fire immunity of Smaug was more a side note. My main point was the size and flight advantage of Smaug. The Book of Lost Tales places a Balrog as double [Glorfindel’s] stature, thus somewhere between 12 and 15 feet tall, while Smaug was somewhere between 65 and 80 feet long. Assuming Smaug didn’t just fly in circles breathing flame - like you would trying to destroy a town built on a lake - and stooped on the Balrog, that’s an incredible amount of force coming to bear. Even grounded, Smaug had a massive, um, mass advantage. On Gandalf not being allowed to confront Smaug due to the limits placed on him a la Sauron - there was nothing wrong with him fighting the Nazgûl, who were Sauron’s ring-servants.
From what I’ve gathered, Smaug’s scale was broken off by a black arrow in the first attack on Dale, from the movie. I don’t believe The Hobbit ever actually explained it.
(Lost Tales also has Tuor, a hero of Man, killing 5 Balrogs by himself. Later notes by Tolkien suggest paring the total number of Balrogs down to less than a dozen.)
[Moderating]
I was initially reluctant to mar such a sublime pun as the one in the title of this thread, even if it was accidental. But it hasn’t provided nearly as much fodder for jokes as I’d expected, and the OP did request that we change it, so I’ve fixed the title.
I think there are various power levels among the balrogs, so Smaug might win against one of the lesser 'rogs. But the odds favor the average balrog.
But I would want to have a stout mountain range between the fight and anything I cared about (such as mine own corpus). It would be fierce and destructive in the extreme.