White Knight Story is not a Kingdom Hearts spinoff, it's an RPG game on its own being made by Level 5 and published by Sony. PS3 exclusive.
For the 3rd or 4th time on this topic, Knight's Story is not White Knight Story. Knight's Story is refering to the secret trailer at the end of KH Final Mix, which is a spinoff series to KH main story. That is the game most people expect to be on the PS3, rather than KH3, due to it's more serious hardcore looking style.
Legend, the PS3 does not have shorter load times than the Wii. KH, an ACTION (key word there) RPG would benefit greatly from motion control sword fighting, and KH would be destroyed by any attempt to change it's graphics much, as it's current graphical style balances on a thin middleground between Disney and Final Fantasy, and any shift further in the Final Fantasy direction will destroy that balance. The graphics can be improved from the PS2 games signifficantly for the Wii without destroying that balance, but any futher development would destroy that cartoony style, leaving really no reasons to put it on the PS3 except for perhaps better sound (But one can argue the immersion of a Wiimote speaker makes the audio on the Wii better too).
So logically, we have: A system capable of playing it without harming the garphical balance, with the largest user base, the largest amount of demographic, a family friendly image, cheap development costs, and a useful motion control system.
On the other side: We have 2 systems that won't sell games with a cutesie art style, cost a lot to develop for, don't have large user bases, don't fit the game's target demographic, and have graphical capabilities that are useless for the game.
The logical system is the Wii. That's not to say that developers always make the logical choice, but the only reason for it not to be on the Wii is "OMG SONY LOYALTY"