Let me try. This is going to be an insanely exaggerated example btw, so I don't want anybody chiming in with "and in what world have you ever seen this happen?".
Imagine that over the space of 1 second, one platform achieves an average framerate of 60. However, in the first half of that second the game was running at 120fps, and completely froze for the second half, creating an average of 60fps. If this was something that was happening on any consistent basis then this games performance wouldn't be preferable to another platform that only had a 45fps average, but had each of those frames spread rather evenly throughout each second.
So basically, the X1 can have a lower minimum (or even average) framerate, without this really being perceived by the player in comparison to the higher fps on the PS4. If the stuttering cause by an uneven distribution of frame times creates a similar perception, then the average framerate becomes mostly meaningless.
One of the best posts in the thread. Based on my limited tech backround, makes sense. The deliverance of smoothness is more pleasing to the eye.