Brace yourself: I'm with Miruvor on this one; the first thing I thought of (as usual when this question comes up) was Feanor, and how he stood until Gothmog himself came. I had the impression Feanor laid about himself, dying the death of a thousand wounds gradually in the process, and that only the coming of Gothmog combined with his wounds prevented it from becoming a one man route of a bunch of Balrogs (which would have been amusing; Feanor was a bad--s.) It seems strange we would know how one out of nine Nazgul met their end, but half the Balrogs.
In a way, it's a GOOD thing the sources are vague; the individual reader can decide questions such as this for themselves, as no one really has the "right" answer. Despite the "name of Fingon" controversy (from what I've heard second hand I'm inclined to go against the Silmarillion for the sake of continuity on that) asserting HoME on Balrogs against the Silmarillions implicatons makes as much sense to me as going with the LT2 version of Beren, so I'm pretty much with Miruvor all the way.
As a side note, I personally think few, if any, of the Third Age Eldar could stack up with those of the First Age, the few of whom around for the War of the Ring were a different class of Elf than their younger fellows. I don't think LotR can be fully appreciated without the Silmarillion, for the reasons cited above. The loss referenced throughout the series is just a concept until you read the Silmarillion, but then becomes something poignant you share, realizing that the glory of the Elves and Edain is past, and the former soon entirely gone forever. Thus, the triumph of Aragorn, his greater similarity to the fathers of his race than to his "peers," and the renewal of his line through Arwen is that much more wonderful.