I don't know the brand at B&C (though I can make a guess due to the ice cream nearly all over WDW and DLR), but at G it's just Dreyers/Edies. G doesn't make their own ice cream. D/E is not something I'm going out of my way for (nor can DH and DS have it, due to ingredients). The chocolate to put ON it at G is, of course, lovely.
But for better ingredients that make up the ice cream, we go for Haagen Dazs.