You talking about Aragorn fighting them off in the 1st movie? Didn't he use fire, and he is one of the most skilled fighters in the trilogy, along with Legolas and Gimli.
As for WK, he does have a monumental reach advantage....and an advantage on top of that. He knows how far his morningstar can go, and he knows that if he misses, his opponent will capitalize on that and try to get in close. It makes sense that he'll be waiting with his sword if she happens to get past the star.
Yeah, Aragorn is a far better fighter than Eowyn and is in truth likely the most skilled sword master in the entire trilogy. He also used a torch against them which is what really won the battle for him.
Also at this time the Witch King was likely more powerful, which is wht he says, "Ths is my hour," when battling Gandalf.