Cyndane won out because Alivia had never dueled before. We've seen damane fight, and they usually fight from a distance. They've never seen inverted weaves (so have no idea how to counter them), and in damane-damane fights there is usually an army to soak up the brunt of the damage (because damane are too valuable to waste).

Cyndane won because she was a better fighter in general. If skill does come into it, remember that of all channelers in the series, Cyndane appears to be the most skilled judging by her feats. By a long shot at that. So the skill difference would have been HUGE. Far greater than between just about any other pair that has fought.