From what I've read and know, the issue is largely with Fox Sports — Oklahoma in particular but also Texas are not happy with Fox. Additionally, they wanted to start working on the next Big 12 TV rights contract and Fox and ESPN declined — that is what started Texas and Oklahoma looking at moving.
I think the only way Texas and Oklahoma would stay is if ESPN offered a "sweetheart" TV deal to the Big 12 to replace the current media rights contract. Instead, it appears that the next Big 12 TV deal will not improve on the current contract, and that is why they are leaving.