I may be wrong, but I don't think it really is anymore. It came out of the gate with a lower price point due to XB One originally bundling Kinect. After they've ditched that though and MS has gotten XB One's price down below PS4's it seems to be picking up. I remember seeing several articles stating that XB One's outsold PS4 over Black Friday, and it may continue to do so over the rest of the holiday season.
At this point PS4 just has a fairly significant lead overall and any ground Microsoft has gained has been minimal - probably not enough get back into the lead in installed base for the remainder of the lifecycle.