Gandalf said that Aragorn and Glorfindel together couldn't defeat the Nazgul on foot. As
Boromir said, it is doubtful whether anyone not wielding the Ring can defeat all Nine by themselves. However, if anyone could do it, I'd back Gandalf the White- he was capable of fighting the Nazgul when he was Gandalf the Grey and he could defeat (albeit, he might not be able to
kill- the prophecy) the Witch-King in the form of Gandalf the White.
As to whether who would win out of Elves and Men, I'd say it's an individual thing. Turin beat Saeros and Beren defeated Celegorm and Curufin, though I'd certainly say that Elves would probably be the superior fighting race, as they are in lore, music, etc.
Remember, the Numenoreans learned a lot from the Eonwe and the Eldar, as well as discovering a lot for themselves, so my bet is that any Elf from the Blessed Realm (and even the 'average' Elf) has a greater chance of defeating a man. However, there are exceptions. It's hard to say who'd win a fight between the 'average' Man and the 'average' Elf, because although Men are said to be stronger, we all know there are many factors in a fight rather than just brute strength- i.e. stamina, speed, skill, etc. It's like asking who would win a fight between Fingolfin and Hurin, or Gil-Galad and Tuor, or Aragorn and Glorfindel- there's no real telling who would win.
To get back to the original question, I would say yes, the Nazgul are stronger than most Elves as a result of the power instilled in them by Sauron's Nine Rings. However, we have seen that some Elves, such as Glorfindel and even Men - specifically Aragorn and Eowyn - have defeated the Nazgul, whether temporarily or in Eowyn's case, for good. Elves born in the Blessed Realm live both in the Ringwraith and 'normal' world and are said to have a great power against the 'shadows of Men' that are the Nazgul.
However, as I said before, this is an individual case, so therefore sweeping generalisations cannot be made. I acknowledge though that Elves are the 'superior race' in general compared to Men. To me, the Nine Rings put the Ulairi (I'm getting sick of saying 'Nazgul' all the time
) on the same plane as most Elves, though people like Elrond, Glorfindel and Galadriel could defeat them individually. Whether they could defeat them in whole group remains to be seen.
EDIT: The Nazgul have an advantage over Men that they can travel unseen and also the advantage of fear. After all, this is said to be the King of the Nazgul's main weapon (aside from that beastly mace- urgh!).