Well if you go by "the chartz" the PS4 is beating the X1 12.4 vs 6.2 esentially doubling the sales. We don't know much the X1 price cut will effect the install base, but I believe the X1 will catch up.
However, you must factor in the US install base as a majority of your MP games will be played against North America. In the US I believe It's a much closer battle with the PS4 leading by 1.5million? (could be wrong there). I don't know how COD did at launch but I read the Destiny numbers were very, very , very close and the only reason PS4 had a slight edge was because of the white destiny bundles. Perhaps 5% more or so from what I read on Neogaf. Perhaps this due to the pro Bungie fanbase of the X1 or because of what you said, MP gmaes on X1? I don't know.
I think in the US online population should be neck and neck, but World Wide the PS4 will have the edge.
I go where my friends go. Almost all of my friends went X1, or X1 with PS4. Very few did the switchover to the PS4, they were already invested in the XBox eco system in terms of the friendslist, achievements, etc. and didn't want to start over per say. System loyalty is pretty rare these days (look at Wii vs Wii U sales lol) but it seems like Microsoft's big push for online has helped the X1 in that sense. I would say the PS4 would probably be outselling the X1 4:1 if it weren't for their online and now aggressive price cuts. It's going to be really interesting to see how the X1 sells in November and December.