Board Thread:Questions and Answers/@comment-118.211.8.204-20150302141811/@comment-26216493-20150319142119

Yuuki has an higher level and combat skill. She also has played VRMMOs longer than Kirto, so you would expect her to win through logical sense.

But only if it was an actual battle, Kirito would have won. I don't believe the creator allow him to lose. Since he is a "Almighty God".