There is no fork in the blockchain and hence the Bitcoin Core and Bitcoin Classics are still on the same branch. This is till at least 75% of the miners vote for the increase in size. Till then, both Bitcoin Core and Classic would be on the same branch and there is no difference using either of them. If you want to switch, you can go to tools>Network and switch to another server.
Doesn't BTC-C have 2MB blocks, though? Surely those blocks mined by BTC-C miners would be rejected by the Core nodes if they were > 1MB?
Bitcoin Classic nodes are modified to see and accept 2MB block. However, until at least 750 out of 1000 past blocks have miners voting for 2MB block limits, the client will still follow the rule of accepting 1MB blocks and below only. There is a 1 month period after the 750 blocks where they will still follow the same chain till Classic starts accepting 2MB and below block.
