The most obvious change would be the transparency of a blockchain.

Currently, when an individual lends funds to a bank, they don't know where that money goes. They simply trust that the bank will be able to return their money when they need it. This trust is usually well-placed, but occasionally a bank doesn't have the funds that their members believe they have. In the United States, the FDIC ensures that most people won't lose their money if this occurs, but this adds more parties into the system making it more complex and expensive.

With the blockchain, you could deposit funds, watch them move throughout the blockchain, and know exactly where they are at any moment. You could also audit the financials of the bank to know if they are financially sound.

It would also reduce the risk of human error, since the blockchain itself acts as the ledger and accounting tool instead of relying on people.