It will be hard for the PS3 to beat the 360 in NA this holiday season...I think it will be virtually even all the way, unless MS drops the price again.
In Others there will be a good surge throughout the holidays. I can see the PS3 being the home console to get this Xmas, although the Wii will continue to dominate again. In the last 6 weeks, the PS3 has outsold the 360 by 2:1 and I can see a similar pattern right through Xmas.
In Japan is where it will make the difference, especially with FFXIII coming out before Xmas. There are apparently 450k pre-orders already and although most of those will be PS3 owners I can see quite a high number of first time buyers getting the PS3 for FFXIII.
All in all, I can only see the gap closing from the current 7.25m to around 5m at best. We won't see the gap getting closer until GOW3 and GT5 come out as these will push more sales....but by this time, MS may have introduced a price cut.
Prediction (June 12th 2017)
Permanent pricedrop for both PS4 Slim and PS4 Pro in October.
PS4 Slim $249 (October 2017)
PS4 Pro $349 (October 2017)