A "central bank cryptocurrency" is like a car being pulled by horses

One of the greatest benefits of Bitcoin is that there are no third-party interruptions. Governments, central banks or other financial institutions have no way to interupt transactions or freeze accounts. Bitcoin is purely peer-to-peer. Bob can make a payment to Alice without a middleman and once the transaction is settled on the blockchain the transaction is irreversable. Once you own it, you own it. No chargebacks.

Owning Bitcoin is different than 'owning' fiat money on a bank account. The money on your bank account is actually a loan to your bank. You don't own your money, the bank owns it. You own a claim on the bank, but if the bank goes bankrupt or decides to freeze your account you can't use the money you thought was yours. In a world of fiat money we have to fully trust the banks while in a world of cryptocurrencies we can put our trust in mathematical cryptography.

Besides Bitcoin and other cryptocurrencies, I am unaware of any other electronic cash system in which your account isn't owned by someone else. Paypal, for example, has the power to freeze the money you hold in your account if they have a suspicion your account has been misused. And remember what happened in Cyprus in 2013. The central bank of Cyprus wanted to recapitalize itself by taking back uninsured deposits larger than $100k.

This is all impossible with Bitcoin; a decentralized currency. No central authority has control, so no one can take it away from you.

Another benefit of Bitcoin is that anyone with an internet connection can use it. The software is open source and there are no restrictions to use it. No censorship. Compare this with opening a bank account.

Central bank backed cryptocurrencies

We don't know yet how central banks worldwide will deal with cryptocurrencies in the future. What we do know is that banks believe in the blockchain technology and are testing with private blockchains to facilitate bank transactions. Private blockchains can be very useful for testing purposes, but in my opinion a private blockchain is actually nothing more than an inefficient database. A private blockchain is not decentralized and doesn't have the benefits I described above. A private blockchain is absolutely not censorship resistant, because it has one or more central authorities that have control over the blockchain. It could be beneficial in some cases, but in case of making payments and holding savings I would rather trust in mathematical cryptography than a central bank (or even people in general).

This is what a "central bank cryptocurrency" looks like.

I think this picture is a good representation of a central bank backed cryptocurrency.

We invented a car (the blockchain), but let's get rid of the engine (decentralisation / the miners) so we can just keep using horses (fiat money).

The future is decentralized!