What roles does Bitcoin Classic have among Core and now BCH?
Bitcoin Classic has the ability to work on both the core-chain and the Bitcoin Cash chain.
You can have two Classic clients running on the same machine and see both your wallets at the same time, even.
I think the market is moving towards Bitcoin Cash because that is Bitcoin as most people that fell in love with it initially understood it. Bitcoin Cash is as Satoshi clearly intended it.
The good thing is that its up to the market now, after developers fighting and arguing for years we finally have an open market of ideas and implementations and the hashpower and money will choose what happens next.