They'd be pretty much neck and neck when the ps4 drops in Japan.

Anyone thinks they can do it?

Not for long.
PS4 needs more Japanese-centric titles... not to mention the overall strength of handhelds in Japan.

One of the main reasons handhelds are so big in Japan (and around the globe, really..) is that generally, a standard family household will have each their own personal handheld, whereas, with consoles usually only one is bought per household. Another reason is that they can take it anywhere, something that Japan has always loved.
I think it could get close at some points, but not for long. 3DS has more Japanese titles, just as Xen said above ^

PS4 doesn't really have system selling software in Japan this year. Aside from Yakuza Ishin but that's also on PS3. PS4 will probably beat the 3DS for a few weeks and then stabilize under it.

No, unless they get like a crazy game such as Monster Hunter, I wouldn't get my hope up against the 3ds.. Initially, yes, but after the hype, down it goes...

i think that sometimes the ps4 will sell more some weeks other 3ds

 Nope. What Japan centric  games does the PS4 have besides Yakuza? None.

For a month or less after launch yes

Am I reading this wrong? I thought the question was asking about WW sales. Everyone is responding about Japan only though.

I say PS4 will be ahead in most weeks. (Again, worldwide)

on the exact week they release, maybe. not afterwards.