Xbox 360 has dominated USA last generation, and people forget that even with all the bad reputation, the higher price cut X1 didn't sell significantly less than the PS4 in here.
In the USA, as of today the Xbox one only sold approximatively only 11 % less than PS4 did
And for the last few weeks X1 sold on par or even slightly more than the PS4.
Considering all the bad reputation surrounding X1, related to its DRM, the higher price, it still managed to hold its own in the US pretty solidly, and even sold more software overall than the PS4.
Now that the price cut has been announced, as well as Halo and the ability to run IE and netflix without paying for gold, I expect it to sell a lot more.
A considerable advantage is that all these announcement, especailly the price cut will convince a lot of xbox 360 owners to upgrade, and considering how well xbox 360 sold in USA, there are many of them.
The current difference between PS4 and X1 in the US is 322004 units.
That means that if xbox starts selling 10k more than it does currently, (only a 20 % increase in sales) or about 60k, it needs only 32 weeks, or 8 months to catch up. Considering that it will sell a lot during Christmas, It will have more units sold in the US by January 2015, and start outselling it from there.
After that it will slowly grow and eventually sell more long than the PS4. (in the US)
EDIT: Many people consider that I claimed that it will outsell the PS4 globally, I only meant in the USA, I apologize for any formulations that lead to further confussion.