[CSteefel]

Another possible argument against one of the three Rings like Nenya making a big difference is that Gandalf was wearing one himself. Here you have a Maia pitted against a Maia, but with one holding one of the 3 Rings. To the extent that the contest between the Balrog and Gandalf was a draw, then it would seem the Ring didn't make a large amount of difference.

However...

Perhaps another way to view the contest between Gandalf and the Balrog is that Gandalf did win finally, but that the mortal part of himself (the form he took on coming to Middle Earth) was the casualty. From this interpretation, Gandalf is really made up of two components: the Maiar (that later becomes Gandalf the White) and the human, which suffers heat and cold and injury like the rest of men.

Where this leaves Galadriel or Glorfindel is less clear, but neither seems to have a clearly human form in the same sense that Gandalf has (for example, Glorfindel still appears as young as a spring chicken despite his 6,000 year age, while Gandalf appears more aged, even if he does age slowly).