I think the banks will approach it differently... they might decentralize the database across several of their branches, to lower the risk of a centralized attack. I would do that, if I
were them. They would be stupid to try to duplicate what the Bitcoin Blockchain already has in it's massive decentralized hashing power and distributed nodes. For customers, I
would just use Bitcoin, and for inter-account transfers between banks, I would use a private decentralized ledger, and run the nodes at the different branches to spread the risk.
Although some banks {CitiCoin} are trying to simulate the Bitcoin Blockchain, and that would be a seriously stupid mistake.