Round 1: Match 3
Zhang vs. Yeoh
Movie: Crouching Tiger, Hidden Dragon
http://www.youtube.com/watch?v=9OxQ-2gR1DU
In a movie initially lauded, now decried for its fight scenes full of flying around and fantasy, this fight is more grounded in reality than any other in the movie. Granted, that doesn't say a whole lot, but in a movie where people are running up plant stems and jumping from rooftop to rooftop, this fight stands out.
VS
Cunningham vs. Rob Roy
Movie: Rob Roy
http://www.youtube.com/watch?v=SVaslN1NiT0
A great movie swordfight if ever there was one. It may not have a lot of visually fancy choreography, but it has a greate sense of realism and psychology to it. They pause, and wait, think the fight out, they run out of breath because swordfighting is tiring. They don't just galavant into it because it's a fight to the death. And rather than the fight being either really close the whole way through or the villain beats up the hero until the hero arbitrarily wins, the better swordfighter gets the upper hand for the great majority of the fight, and then the hero wins in a somewhat ingenious move that might not have worked if the villain had chosen a different sword. This is one of the two really great swordfights I've seen in movies.