Settling things with a light saber duel was a callback to the days of chivalry when gentlemen would settle disputes by dueling with swords. One could argue that Darth Vader wasn't a gentleman by any means, and being a super evil guy and all that, wouldn't necessarily play by the rules. But I always liked that he had enough respect for his old master to settle things in the time-honored fashion, even if he planned on slicing the guy to pieces.