Board Thread:General Discussion/@comment-96.224.225.28-20141201044200/@comment-1173941-20141201045937

Him cutting magic, and her not, isn't really a measure of who's a better fighter. Kirito simply figured out an interesting game mechanic, and used it. Yuuki never bothered to try (on screen).

And like Dim said-- Word of God says Yuuki is stronger, and better.