People will go for whats convenient so a 'bank-coin' which is well integrated into their everyday banking will be their choice instead of bitcoin. Some of the banks are already working together so they can set a certain standard between them so that your coin from bank A will also be accepted and work with bank B etc...
Similar with digital currencies launched by the various countries like Ecuador, Scotland etc... Few people truly understand what it is that makes bitcoin so unique and different from any of these other digital currencies.
I however do believe that bitcoin adoption will grow over time and especially so if and when some of these 'fiat coins' go down with their creators as that is bound to happen in the [near] future. The moment the first one goes down people will start to realize that bitcoin is still standing and that will in time drive adoption on a far larger scale. All you need is for the first 'bank-coin' to go 'tits-up'.
There are two outcomes:
Either the banks have their own centralized coin, which is only secure if they strictly hold their own control. They will sooner or later face the same fate as AOL in this case. On top of that there's huge security risks this way.
They could alternatively make an open decentralized coin, but that means they'd give up control, which is exactly what they want to avoid. Also, if they do this, bitcoiners would soon control the entire network with their quadrillions of hashing power.