I think Nintendo will loose the battle this year and maybe half of next year. Casuals and many gamers just don't see a reason to upgrade to a 3DS. But next year I suspect Nintendo will cut the 3DS price by 50$ making it 199.99$, stop supporting DS and with alot of heavy hitting titles take back the lead from Sony.
I think Nintendo over under estimates the casuals. A casual gamer isn't about to shell out 250$ for a handheld when their are still good games coming. Also alot of casuals don't even realize 3DS is a new console alot of them think that its a 3D DS. Then theirs the core gamers but right now the software just isn't their and for a price of 250$ alot of them are turned off.
But a good price cut, some new games and a reduction to DS support coupled with good marketing will take 3DS back above Vita.
Also the hype for Vita isn't even as big as the hype for 3DS was. If were going by hype PSP:Vita is dead in the water.
I expect this war to be much closer then the DS VS PSP war was. Sony will actually have a fighting chance if Nintendo screws up even the slightest!