What can blockchain do that normal databases systems won't? Aside from cryptocurrencies, what advantages may blockchain(either public or private) have and real life use cases that can be more useful implemented in blockchain over traditional databases based systems ?
Blockchains are data structures, whose only advantage is that storing data in that structure allows you to achieve decentralization under certain conditions.

So your question reduces to "how is decentralization important"? 
Decentralized systems tend to have the following favorable attributes:


Open (anyone can participate; not permissioned)
Borderless (as long as you can reach one other connected node, country/regional borders don't matter)
Neutral (the system doesn't care what you use it for)
Censorship Resistance (transactions/data entry is unstoppable)
Trustless (falsified data is easily detectable by verifying across multiple nodes)
Immutability (data cannot be removed or altered)
Public