This is not a close fight at all.Bruenor/Drizzt win hands down. If we are talking current forms, it a down right slaughter. In fact you could likely have the entire lord of the rings group minus gandolf and still they would lose.
A better match up would include Aragorn and Gimli versus Bruenor and Drizzt. Though I'm not sure Gimli could defeat Bruenor easily if at all (Bruenor's tolerance for pain is off the charts), Aragorn is the only one of the Fellowship who is renowned as a fighter (Being untouched in the final battle in the books despite being vastly outnumbered).
I agree that be a cooler match up. Though the result would be much of the same.
Bruenor would down right slaughter Gimli, he significantly better in ever single way. Aragorn would get slaughter by Drizzt as well. In fact both Gimli and Aragon would lose even if they both took on Bruenor. And it would not even take that long for him to win either.
Also that part you said about Aragorn is not true. In fact prior to the lord of the ring events, Aragorn was pretty unknown by the majority of his world. Boromir was by far the most famous warrior of the group (most famous not best). Also only character to get praise for his fighting skill in the book by another party member is Gimli who Aragorn alludes to being the best axe fighter he has ever seen. So if anything the suggestion that has been made by the books is that Gimli is the best fighter of the group. Aragorn also does become most renowned at the end of the books, but not as a fighter, but as being the true king of men.
Aragorn was unknown because he had to be. As Thorongil, Aragorn wondered Middle-Earth, and is renowned in Rohan and Gondor for aiding them against their enemies. His greatest highlight under this alias is most likely his surprise attack against the Corsairs of Umbar, destroying several hundred ships with just a few of his own from Gondor's navy.