As we move into bitcoin economy , where there is merchant adoption universally and you are able to buy anything with bitcoin, there is no point an average guy would put his savings in a bank, He could save even a million dollars worth of money in a encrypted paper wallet.
Now banks will lose all the minimum balance that it recommends for having an account, Now banks will not have any money to loan out and hence the entire banking system collapses.
On the other side bitcoin 2.0 applications like counterparty, ethereum will enable crowdfunding and other financial derivatives and decentralized exchanges which will affect the investment banks. Because you don't rely on a central institution like banks to raise your capital.
What other ways could banks face disruption by bitcoin?
What if banks offered competitive interest rates on deposited fiat?
BUt the interest rate is a gimmick, consider inflation which washes away any gains with interest.
but no competitive stratergy can help a inflationary asset like us dollar can fight a deflationary assets like bitcoin