The PS4 has a better shot than before at taking North America, mostly thanks to Microsoft's missteps. It's going to be close, I think, a lot closer than PS3/360, regardless of who comes out on top.
The key will probably be if Microsoft's strategy of turning the Xbox into an entertainment center/set-top box for gamers and casuals alike pays off. I really have no idea what casuals are going to do, and neither do they until they actually do it. Personally, I don't think Kinect 2.0 will generate nearly as much interest as the Wii or Kinect 1.0--especially considering the price. A lot of the people who bought into motion controls were fad followers who have moved on by this point.
Globally, Sony will win.