We are talking about a proper monetary system in which the agents, traditionally represented by Central Banks and financial institutions, are replaced by the rules itself of the system. Those rules are in turn determined by encryption techniques, so that there is a plurality of agents none of which governs each other.
Here comes the first, glaring and structural difference with respect to the classical, FIAT currencies: cryptocurrencies are decentralised by nature. There is no Central Bank regulating, therefore the currency does not depend on the decisions of anyone. This is a major plus for anyone looking for transparency and security. Once the rules underlying the system have been determined and specified, there is no fear of its functioning being modified and altered according to personal interests.
Transparency can also be found in the rules generally governating cryptocurrencies, given that the defining code is generally open source. Therefore, anyone can understand how the currency operates. Moreover, it is usually possible for everyone to see every transaction made for a determined currency, obviously enhancing transparency.
Nodes are rewarded for being an efficient and trusted part of the system, therefore the particular rules governing cryptocurrencies ensure that those nodes have the only economical interest to contribute to the system in a healthy way. The interests of every agent of the system are not conflicting, so the health of the system itself is assured along with its security.
If that was not enough, cryptocurrencies also offer the advantage of transactions executed with great quickness compared with usual transactions operated by banks. Transactions are usually completed within minutes and with an everyday increasing rapidity, while a bank trasfer can take several days.