With cheap fees, it will both happen to BTC and BCH or BCC in some quarters because if that wont happen then I don't see any need for this whole scenario in the first place but that does not mean it will be adopted massively even if its cheaper than BTC because there are several major exchanges not supporting the coin which might limits its use thereby its popularity. Hopefully, in the coming days things will get clearer and everyone will be able to decide the direction to follow.