Actually hypothetically the
nazgul could win in a fight with a
balrog. You see
Gandalf the grey and the Balrog he found in
Moria were near the same rank in ME angel ranking standards, but
Gandalf the WHITE still lost to the witchking. now this has always bugged me because
the nine are not even angels in ME, but then i thought wouldn't it make sense if the nine drew power from
Sauron? their souls are bound to
the ring (and thus Sauron who outclasses Gandalf) so it would make sense if sauron needed it he could send power to help his servants if they got in trouble,
Balrogs have no such connection with Sauron and any benifit they possibly could have gained from
morgoth would be null. So if a balrog decided to fight the nine sauron could just send in some power to help and they could have a chance killing it (assuming they had the
witch king with them).