They both have advantages and disadvantages over each other if you think of it.
Bitcoin banking is more secure than normal banking, because you are the only one that has access to your personal wallet but in normal banking customer cares can login into your bank account without you're notice and use your money for any kind of businesses.
Personal security matters a lot with bitcoins, If your bitcoins gets lost, they are lost for real and the chances of recovery are very close to zero. But with normal banking your funds can be recovered and the culprits even apprehended.
bitcoin banking is more reliable than normal banking because money that is in your normal banking can be deducted or withdrawal without you're notice but that can not happen in Bitcoin banking everything happens with your authorization.
Banks have picked up this habit of some unnecessary charges that they deduct without notifying you simply because you signed to some terms and conditions. With Bitcoins, there are no unnecessary charges.