The real difference is just that it's a database, with no single person/entity in control. So in the case of banks: A bank can arbitrarily raise fees, a blockchain only does so if the majority of the public running it comes to a consensus on doing so. A bank can freeze your assets if they don't like a recent purchase, a blockchain can't. A bank will usually make sending money to friends or family across borders extremely slow and expensive, a blockchain won't. A bank might not accept transfers on holidays, a blockchain is up 24/7/365 globally.

At the same time: A blockchain will be so public, that all transactions can be seen by anyone. With your bank, your transactions are only visible to them (and whoever they sell them to). (Unless you use a private currency like Monero or Zcash) A blockchain will usually be slower for redundancy, a bank's database won't. A blockchain records data permanently, a bank can delete data you don't want after a certain period of time.

It's really just different databases for different use cases. Many people in developing countries use crypto for daily purchases because banks won't give them accounts, and at the same time, many people won't use crypto for everyday purchases in places like the U.S. because their bank's infrastructure is faster and more convenient.

I personally have had more success sending money to friends, paying for my VPN, and spending money on holidays, using crypto rails, compared to my bank, but I've also had more success with everyday purchases using my bank, because it's just more convenient.

The gist is really just that blockchains are a ton of computers everywhere recording the same list of transactions permanently, under a certain set of rules, and a normal database is just that, but under one person/company's control, with more arbitrarily change-able rules. Your use of them is really just up to your preference regarding security, privacy, speed, and reliability.