How many weeks will it take the PS4 to outsell the WiiU in each region?

[eFKac]

Europe week 1 if supply is enough and should stay like that for the rest of the generation.
NA I possibly see PS4 do it sometime around early next year temporarily, with Wii U regaining the lead when DKCR, Mario Kart and Smash combo release.
Rest of the World is a tricky one, cause I actually don't know which countries it launches in, but shouldn't take long, that's where PlayStation is the power.
And Japan obviously the longest, maybe sometime 2014, maybe 2015, after a pretty strong launch week I expect it to struggle like Wii U did there cause of lack of Japanese centric software, especially exclusive to PS4. Both consoles will sell badly there.