The bitcoin could win at the end of the journey but right now the dollar is just too big to do this.
It would take many years to achieve this mission.
The bitcoin or other crypto currencies might win in a few decades. But the fiat will still be there for long time.
We cant compare bitcoin with dollar, dollar is more stable than bitcoin. Bitcoin is highly volatile, but such a value is the reason for highly preferable, but bitcoin is not much of a currency , it is being used like an investment.