You can assume that everyone will immediately update to Classic nodes and therefore that only one chain will survive. But that's unlikely. I sure won't be updating.
You'll probably be
DUMPING!!! 
Well, that depends how it pans out.

Yes, dumping is a realistic option. So is double spending on one chain vs. the other. Or some combination. It will be interesting if the hard fork breaks consensus, I'll say that much.
I know that I will be dumping both chains if we fork to a new client.