rays.... quarter sawn parts are more stable because of the rays. these are structures that run from the pith out to the bark.
White oak is used for barrels not because of it's quarter sawn or ray character but because of it's tyloses and strength. it is stronger than other woods and the tyloses block the pores making it water proof. it is also favored for it's flavoring aspect.
the lack of tyloses is why you never see a red oak barrel.
i recommend reading or perusing "Understanding Wood" by Bruce Hoadley