In both cases the trading value of the currency has almost nothing to do with who originated it, and almost everything to do with how the general public feels about it.

Just like crypto, most "government" currencies are worth what they're worth only because everyone agrees that they are. That's called "fiat" currency. And that's why fiat currency exchange markets exist. The US Dollar hasn't been "convertible" (redeemable for a fixed amount of precious metal) since 1971, and many other world currencies were already backed in some way by the US Dollar at that time.

The real difference is in the supply.

Government fiat currency is difficult to counterfeit, although the government (or reserve bank) can always make more whenever they want. We trust them not to print more money, increasing the money supply and devaluing the currency. However, this is exactly what has happened sometimes in the past, and no doubt will happen again in the future.

Crypto currency is virtually impossible to counterfeit, and IIRC there's a finite (but not precisely known) amount of it that can be made, no matter who you are.

Personally, I still use physical fiat currency and no crypto. I'd like to use crypto, but regulation in my country makes it very difficult to use without registering your details with a central authority. And although everyone's pushing e-money options which are similarly tracked, thankfully I still have the option of using anonymous cash.

I don't do anything bad or illegal. I just believe that government and big business don't deserve to know everything I do in my life simply because they want to.

Crypto doesn't have value because tech bros say it does, that's not how it works.