One isn't really any better than the other. Unless, of course, you're a fanboy.
Look at the game set, and decide from there. I bought the PS4 when it was time to upgrade. My primary reason was for the Gran Tourismo franchise, since racing games are my thing. Waited a year after getting my PS4 for the newest version, just to find out it sucks. Now I wish I'd have bought the Xbox so I could have Forza instead. Such is life. There's still a bunch of good games.
So look at the platform specific franchises. See which platform offers the game you (or the kids) really want, and go from there. As for the cross-platform stuff, unless you're a hardcore gamer (in which case you'd already have both systems) you won't notice any real difference in gameplay.