[Gordis]

As far as I remember, it was not Sauron, but Gothmog the Balrog who was head of Morgoth's army. So who of the two was Morgoth's second remains a question.

Also we don't know if Sauron had been friends with Gothmog and other balrogs back in the First Age. They might have been bitter rivals.

I am not sure that Sauron himself would fare well if pitted one to one against a Balrog, even the Moria one, much less Gothmog. In the Third Age Sauron was fully incarnated, even self-reincarnated (twice) and that weakens a Maia. The Balrog was likely still a shape-shifter. Sauron might have won, but it would cost him dear.

Eönwë: Err... Gandalf? But then again, no-one except Cirdan knew exactly what he was.

The Witch-King likely knew exactly what Gandalf was. He had a long experience of observing the Maia Sauron at close quarters. Here is also this quote from "The Hunt for the Ring":

Oct. 3: Gandalf reaches Weathertop but does not overtake the Witch-king and other four Riders; for they become aware of his approach as he overtakes them on Shadowfax, and withdraw into hiding beside the road. They close in behind. The Witch-king is both pleased and puzzled. For a while he had been in great fear, thinking that by some means Gandalf had got possession of the Ring and was now the Bearer; but as Gandalf passes he is aware that Gandalf has not got the Ring. What is he pursuing? He himself must be after the escaping Bearer; and it must therefore somehow have gone on far ahead. But Gandalf is a great power and enemy. He must be dealt with, and yet that needs great force. - RC p.167

Eönwë:Yes, without Sauron he's just a mortal, however powerful and sorcerous (is that a word?). I think he still has the Gift of Men, however long it takes to reach him. A Maia is a Maia and cannot be truly killed- ever. Even an elf can't, so what makes anyone think a mere man, however powerful, could match a Maia.

The Witch-King had no idea that the One Ring was about to be unmade. While the Ring existed and the Nine Rings had power, the Gift of Men was not available to the Nazgul. If killed, they would likely become powerless spirits without a hroa, roaming Middle-Earth but unable to interact with the World of Light in any way - and that until the Rings existed. Basically it would be the same fate as for the Balrog or another wayward Maia when it is killed - eternal misery.
Nothing to look forward to, thus the Witch-King must have been much more reluctant to die than any mortal Man. He never fought against a stronger opponent when he could help it.

As for mortal Men, they were not as weak as some tend to think. Three Men killed a dragon (Turin, Fram and Bard), yet we know of no elf who had achieved the same. Beren fought Celegorm and Curufin and was in Angband, there were Turin, Tuor Elendil... but you know the story.

The Witch-King still had the same body he was born with. Albeit invisible, he had the high stature and strong muscles of a High Numenorean lord - and those were quite similar to Elves:

The Númenóreans, Kings among Men ... grew wise and glorious, and in all things more like to the Firstborn than any other of the kindreds of Men; and they were tall, taller than the tallest of the sons of Middle-earth; and the light of their eyes was like the bright stars.-Akallabeth

On the plus side he had his sorcery, lots of experience, sharp senses and extra-endurence of a wraith. On the minus side he had his fear of fire (important against a Balrog) and his fear of death.
I would say he had some chances against the Balrog - at least to make it even.