the X1 has more robust media features than the PS4. now, that could change if/when Sony ever decides to add those features to the PS4. but, it would still lack all that TV integration stuff.
so, if you want your console to do more than just games, and you want it to be your enterntainment hub, then the X1 might be a better choice. that's a legit reason for the right consumer.
another reason. MS is more transparent and frequent in updating the X1. As a PS4 owner, that's prob my biggest peeve. At least with the X1, you have a reasonable expectation that they will keep on adding features and improving the console.
also, as far as multiplats performing better on the PS4, it's debatable how much better they are on the PS4. everyone's harping on the whole 1080p vs 900p or whatever.
but, I played DAI first on the X1. then switched over to the PS4. The PS4 version looked and performed pretty much the same as the X1 version.
I didn't notice a dramatic increase in graphical/performance quality.
so, in reality, unless you analyze the frames and resolutions in minute detail for a living, I think you'd be hardpressed to notice any significant difference.