I'm not sure any sufficiently 'magical' blade, even in the hand of a powerful being like Aragorn or Gandalf , could have killed Angmar. He is not simply a superhumanly powerful being, but a living symbol of Evil. The destruction of Evil (in Middle-earth at least) is not a matter of mere power (cf The Ring). A living symbol needs a symbolic death.
What we have is a symbolic event. It has to do with what Angmar symbolises to those who confront him - specifically, in this case, what he symbolises to Merry & Eowyn. To Eowyn in particular he symbolises her despair, her severe depression, the death she seeks. To Merry he symbolises all he fears, a manifestation of the 'unsupportable weight of Middle-earth' he felt back in Rohan. Their combined defiance, their refusal to be swallowed by the void he represents, is what inspires them to act. Both fight in defence of one they love - Theoden (in Merry's case also his love of Eowyn). They stand in the face of Death, 'the inevitability of Death' as Tolkien put it.
Thus, to reduce it to questions of 'power' is to miss the point. It is not simply the Blade of Westernesse that makes Angmar vulnerable to Eowyn's death-blow. It is that blade in the hand of Merry, with the desperation (& desperate hope) behind the blow he strikes. Had the blade remained in the Barrow it would have been useless - it became Angmar's bane in the hand of Merry on the Field of Pelennor. Eowyn's blade would have been nothing but a sliver of metal if she had not ridden as Dernhelm in search of Death ('Do you not know Death when you see it?').
It is the defiance of Death, inevitable Death, in the heart of an Hobbit & a Woman, that kills Angmar. But it is also the defiance of Death in the heart of the Man who made the Barrow Blade, & wound it about with spells for the bane of Mordor. It cannot be reduced to Gandalf was powerful enough to do it, or Aragorn was powerful enough.
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