For me, BCH will not overcome BTC because BTC is the origin of all cryptocurrency. Also, BTC has a very large value that BCH can't reach but I am hoping that BCH will increase its value even not more or equal to BTC's value at least BCH will have a good price.
You do have a point there, mate. Bitcoin will always be the most prominent cryptocurrency on the markets, since it is the original cryptocurrency which brought us the blockchain technology. Without it, many of the cryptocurrencies we know and love today wouldn't have been possible. Considering that BCH is just a fork from the original Bitcoin blockchain, it may never replace it, the same way ETC never replaced the original Ethereum.
Therefore, I believe that in the future both of these cryptocurrencies will co-exist (Bitcoin and Bitcoin Cash) providing people with options whenever they want to quickly send a transaction or just secure their investments for the long term. Whenever it is Gold (BTC) or Cash (BCH), there will always be a choice for anyone to transact in this rapidly evolving technology. Just my thoughts
The thing that makes Bitcoin Cash distinguish from Bitcoin is the ability to send fast transaction and the chance to host more transactions in one block, or that's what they told.
After 2016 blocks of fast transaction, there will be few days of very slow transaction since the difficulty increased drive the miners switch to mine Bitcoin instead of Bitcoin Cash. Mining Bitcoin Cash will only be more profit than mining Bitcoin after the Emergency Difficulty Adjustment.
Who will benefit from this kind of arrangement? Miners. There's no coincidence that people calling Bitcoin Cash the Miner's Bitcoin.
This makes the Bitcoin Cash a much less reliable comparing to Bitcoin.
So, to the question laid by OP, the answer is no way.