Hmm, well on the side of the Balrog, we have him destroying the entirety of Khazad-Dum and forcing Durin's folk to flee, who up until that time had been likely the greatest Dwarf Kingdom of Middle-Earth. We're not talking some sudden thing either; it took nearly three years for the Dwarves to be driven out of the halls, if I remember correctly, which is plenty of time for them to have marshaled all the forces they could, and those forces to have been defeated. It also assuredly fought in the War of the Jewels, and survived, no small feat. Furthermore, It broke Gandalf's spell at the Chamber of Mazarbul, one of the more powerful Maia of Manwe, and was only eventually slain in full by being cast off the top of an environmental hazard, not in direct combat. Even defeating it slew Gandalf, again one of the Istari chosen for their power and wisdom to oppose Sauron.
On Galadriel's side, she is a High Elf, and saw Valinor, which gives her power against the spirits of Arda. She also bears an Elven ring of no insignificant power, though its ability to aid her directly in war is left undetermined and dubious; it seems more likely that the power of Lorien lay in the enchantments woven about it, which to my mind would be similar in form to those of the Girdle. We have canonical examples of Elves defeating Balrogs. They are not many in number, and whether or not those Balrog's had slain many Elves ere they were brought down is obviously a matter for debate. We know that the Elves are the most powerful created beings of Arda, and obviously had the ability to move against what they knew as the "Nameless Terror".
Hmm. Though, in the book, and on the wiki, it seems that no part of the outside world is actually aware that the Balrog is, in point of fact, a Balrog.
