They may be separate but they are not unrelated. There is only so much mining power and its distribution affects both (actually all) chains.
Speaking of which BCC has reach the price (0.153 BTC), calculated on reddit by Jonathan Vaage, at which mining on BCC (including all costs and rewards) is better. This has become a rallying and resistance level and the battle has been joined between these armies of miners, traders, whales, etc.
The next scheduled (not 20% emergency) difficulty adjustment comes in just a few days for BCC (could be this weekend). After that, BTC also adjusts in a few days. If a flippening is in the offing I think it would come shortly after the BTC adjustment. If the miners in a major cartel then flee to BCC, it will leave BTC bereft of hash power and block intervals could explode preventing any practical use of the blockchain (a Chain Death Spiral). If so, Core supporters will probably be forced into using similar "emergency" difficult adjustments (even though they tried to humiliate Cash advocates about this methodology before the fork).