I think that bitcoin can not compete with cash, because it's two different directions. They can exist in parallel complementing each other, but not destroying each other.
Are you discussing bitcoin cash or just regular cash? Because those are really two different, so different, things.
If you are really talking about cash as in fiat, right now bitcoins can't surpass it. But just wait.
Bitcoin cash on the other hand will never surpass bitcoins, I don't think it will ever be able to.
I suppose this will come down to whether SegWit2x can handle the growing transaction volume. BCH's entire premise is that BTC won't be able to scale suitably, and that's why they split off, to enact changes the better handle growing transaction volume. It's far too early to tell if it will have staying power, but if BTC can't handle transaction volume growth, or the network becomes over congested like it was for a large portion of this year with sky high transaction fees, it's going to give BCH a large validation that the split was necessary and BTC didn't do enough to address the problem. Unfortunately, with the amount of money at stake in both chains, BCH is incentivized to try and sabotage the BTC blockchain at this point to make it unusable and drive people to BCH, thus increasing the value of the BCH tokens. I think it's more than likely that we're going to see attacks by both sides attempting to undermine the other, and that overall is going to be terrible for BTC/BCH and crypto generally.
Currently we see crazy growth for today, I'm going to enter after the first dump 
