It should be mentioned that Harry Potter characters have trouble with monster like the Baslilisk and the dragons in Goblet of Fire. So I'd say Snape would just annoy the Balrog until it catches him and eats him.
I'd guess the reason HP characters don't just do away with their enemies with Avada Kedavra, as say Voldemort would, is because the Ministry has ways of knowing if they cast spells and they are forbidden even on non-humans, and as Slughorn says to take someone's life splits your own soul, or something.
However nothing has ever survived the killing curse save Harry Potter, and that means giants, dragons, giant spiders, centaur, anything.
We'd need clear descriptions on the extent of magic resistance for the Balrogs.
There's no reason to believe that Rowling magic would be somehow ineffective against Tolkein magic; rather we should examine the extent to which Durin's Bane was able to resist, say, a lightning bolt from Gandalf, and compare it to a lightning bolt from Voldemort or whoever.
Regardless, I think Snape is slightly more battle savvy than Gandalf, as he is very mobile and has high destructive power against single opponents. He also has 2 hour prep, compared to what Gandalf had, which was horrible conditions...