There is one important difference between fiat money and cryptocurrency, which is, fiat money is basis of production and investment decisions, basis of costs of doing business and setting of product prices or investment returns. These activities contribute towards determination of the value of a currency.
Interest rates are utilized for management of currency valuations primarily via their affects on production and investment decisions, not via any direct effect on value of a currency. Until cryptocurrency becomes basis of production and investment decisions, its value is primarily driven by demand and supply, as opposed to secondarily driven by demand and supply.
The value of fiat money is primarily determined by confluence of production and investment activities within countries, and only secondarily determined by demand and supply either within or across countries. It already is well established in Economics that money supply is not primary determinant of inflation or interest rates. In this important difference lies continued superiority of fiat money over cryptocurrency.
That being said, cryptocurrency has value in realm of need for hiding of identities behind transactions or for people who seek to store value that is more difficult to confisticate than fiat money. In an imperfect world, there can be legitimate rationales for such motives. Unfortunately, transition of cryptocurrency to basis of production and investment decisions likely reduces room for anonymity of transactions, as such likely eats at the core value of the concept.
It is important to be aware that issuers of cryptocurrency are not created equal. Just as companies are judged on basis of going concern so also it is important to assess going concern properties of issuers of cryptocurrency.