So which is it?
There are many factors at work here, some of which we may not get answers to until Episode VIII, or not at all. So here's what I think.
1. Kylo Ren was not interested in defeating Rey. He was not fighting to win, he was trying to get her to join him ala Darth Vader vs. Luke Skywalker. We are pretty certain that Kylo went all Anakin Skywalker on Luke's Jedi cadets killing all his Jedi trainees... except perhaps a young Rey so yes, Kylo is a powerful Sith by the time he duels Rey and should be expected to win.
2. Not too long before the lightsaber duel Kylo was shot in the left midsection by Chewbaca with his bowcaster. The Force Awakens made sure to point out that this was a powerful weapon. Kudos to Kylo for not immediately seeking medical attention showing his toughness. However, the injury most certainly played a role as seen in the final moments of the duel when Rey appeared to be stronger.
There you have it. Kylo was severely injured and not interested in defeating Rey. Mystery solved. Can't wait to see Star Wars Episode VIII.