I expect the PS4 version to look and/or run better, but the XO version to have bigger MP maps, more players etc. At least if the dedicated servers thing is true, but we don't know yet. If they look/run the same, something is afoul because the PS4 has a very easily accessible and apparent hardware advantage. Not a small one either.
advantage yes mostly GPU (and in case you were wondering I don not believe GPU Down clock

but CPU is the same in both machines for all intents and purposes (beyond customizations)
so there could be many games where the cpu is a factor and GPU less so
edit:
also yes agree with you that the dedicated servers may come into play in many of these big MP games
the cloud is more than running MP host on a dedicated server though it scales and allows non latency compute to be taken as needed from several servers to compute parts of game, but you know that already 
