A blockchain is always more secure than a Centralized system and is beneficial for several reasons.
If you have some sensitive data you don't want to lose it. Blockchain can act as a backup service for your data.
A node goes down the data is still there, that easy. For a private blockchain, it builds trust. Imagine a finance company or a bank. Since the customers have a copy of the data and it's not centrally controlled by the bank they would trust it more. Also, have a look at smart contracts. They are one of the key points that makes a private blockchain extremely powerful.