PS4 will very likely outsell Xbox1 globally. Xbox360 had about 1 year headstart, and PS3 still outsold xbox360 globally, so I don't see the next gen xbox outselling PS4 globally, especially since xbox1 won't have a headstart in release like the current gen. However, Xbox360 outsold PS3 almost 2-to-1 here in the states, and xbox360 still outsell PS3 weekly here.
Although Xbox1 is getting lots of bad press and rage from internet forums, I'm not quite sure that PS4 is going to outsell the Xbone in the states. The yearly Call of Duty releases have so much internet hate from video game fan forums, but the the majority (if not almost all) American video gamers don't care, and much of COD sales are from the US. All the badmouthing from VGChartz forum posters virtually had no effect in sales of COD games. The internet video game forum posters are representative of much less than 1% of the average consumer. Most video game consumers don't come to places like VGChartz to get their info. So that's why I don't think all the internet rage at Xbox1 will not affect much of Xbox1 sales in the US.