I think the problem for sony still is ps3 library. Even if they have bc i doubt they will have ps5 bc with ps3 (speculating mainly).I'm saying Microsoft have the BC thing going for them, if Sony get even close to being on part BC wise next gen that's a major advantage for Microsoft lost.
+ Microsoft on there next box will have xbox + xbox 360 + xbox one titles bc (again speculating). Also to be honest as much as i want this in grand scheme of things BC means very little. New fresh exclusives will always triumph bc.