.....Yo, this is my first post so i can get us back on subject. The Longsword would probably snap the Katana in pieces with one strike, and would liquify the dudes insides if it made contact. The Katana is more agile however, and all it would take is one nick in the throat or femoral artery and the guys dead in a few minutes.
Also just a fact. Mail could stand up to an ultra-sharp Katana with a huge blow, and plate would be even better.
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Its nice to have an educated opinion on this otherwise unscholarly thread.