What two competing systems? FRB will exist regardless of whether the asset is $, BTC, or metal.>
Nope, the FRB could survive a longer run only if there is an entity of last-resort-lender, which has an ability to create new units of money out of nothing (i.e. in current fiat money systems - those are the central banks - which uses that to do the bailouts of otherwise failed institutions on regular basis).
With bitcoin no such entity like central bank could possible exist. There is no way to create new bitcoins on demand out of nothing, that's the beauty of it.