Fear and Physical
Although, despite being able to overcome the fear that the Nazgul create, you still must have suitable skill to defeat them in combat. They have been around for a long time, and I don't doubt they have gained plenty of experience using weapons. So there are really two stages of battle, overcoming the fear, and then overcoming the physical.
So whereas Glorfindel was able to fend them off with just the light of his presence, Gandalf, Elrond, Imrahil, Aragorn, and the others who had not seen the Trees would actually have to push them back physically(Elrond used a river, Aragorn his sword and voice). So it also does matter how much skill you have, not just being able to master your fear.
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