Probably PS3. They must have a reasonable part of the game ready, shifting to a architecturally different next gen would demand remading it from scratch. Since FFXIII series isn't very succesfull, it's better to made a new one for PS4/720 with different characters and launch Versus on PS3 or simply cancel it.

I oughta just cancel it. I guess they can start from scratch and make it for the PS4. If it comes out for the PS3, it needs to come out before PS4 is released, or it'll be dead on arrival. Nothing thus far suggest that Versus 13 will be released anytime soon or before PS4 is released.

The same day that Netscape 10.05 arrives on Black Berry.

or maybe until we stop buying them...

Nope.
As they said nearly every team had to help the FF14 Team so the reboot wouldn't take as long.
They said nearly everyone of Team Nomura had to go over there.
If that game wouldn't have failed so hard in its 1st Release this wouldn't be needed.

At the same time of course they can make a cheap Lightning Returns...They said it only takes them 1 year cause they just do random garbage.
Sales show how bad those games now sell but they need to throw something out....at least in their opinion.
They rather waste money and destroy their franchisename further.

And i think Team Nomura isn't that unhappy about wasting time.
As we all know Wada talked with Microsoft about Versus13 and this was the last time we heard something new about Versus13.
Nomura is a visionary person - He wanted always to make a perfect game for the best HD Console available with his style.He know he can't go all out with a Multiplatform game(except if its for PC and PS3) and rather stalls the development before he has to downgrade to much.
As we know in the latest news long time ago Nomura said Versus13 will use some parts of the new Luminous Engine.
I can imagine Wada and Team Nomura agreed with a NextGen Release cause the NextBox will probably be able to run a PS3 Exclusive.Maybe they are starting to change the whole game into the Luminous Engine.
It won't probably stay Exclusive but it won't need to with Next Gen...A early NextGen Game won't be able to use all the power the PS4 has and so the versions wouldn't be so different but it will still look as good as a PS3 Exclusive at least.
Wada needs money to finance the next "Lightning Returns for the last time now with CoD Mappacks" Edition.

there really isn't a big enough difference between the 360 and ps3 for most of that to be true.  biggest difference would be the blu ray vs dvd disc space.  So I doubt that has anything to do with it.  

It's much more likely that it was a concept that they never had time to properly explore.  Too busy on other stuff, like final fantasy XIV crap...

after or before the ps4 comes out?

FFXIII Versus staff is helping with Final Fantasy XIV: A Realm Reborn, and Lightning Returns.

Final Fantasy XIV: A Realm Reborn development team consist of over 300 members. I assume when they're finish with getting FFXIV up and running, development/production with Versus XIII will shift into high gear.

It'll be out on PS3 in 2014, possible renamed as Final Fantasy XV. The 2011 trailer showed a LOT of progress, I doubt they'll shift it to next gen when it's so far into development. There is nothing wrong with releasing a big title soon after next gen consoles have released, Final Fantasy XII did, and that sold fine.