The difference or advantages of a Private Blockchain over a shared/distributed database.
Private blockchain:
Advantages;
-High TPS: large spikes in transaction costs are unlikely
-Trust (both a pro/con)
-Reliable: can maximize uptime/transaction speeds
Disadvantages;
-money: requires far more money to add nodes to a private blockchain. Networks like BTC/ETH, anyone can go and become a node to add to the network. Private blockchains can't scale as well.
-Highly prone to manipulation: trasnactions can be changed, users can be blocked, etc.

Public Blockchain:
Advantages;
-immutable: nothing on the network can be changed
-transparency: anyone in the world can go and read transactions, and be a part of the consensus process- whether it's PoW, PoS, BFT, etc.
-Decentralization: No single party can control/edit a blockchain.
Disadvantage;
-TPS: some public blockchains aren't very scalable yet (key word here is 'yet')
-Transaction cost: sometimes gas fees can be extremely expensive. Back in 2017 sending BTC could cost $20-30. It's far less now (less than $1 usually), but during high level of consumption, it can be more expensive. These costs are quickly decreasing as well on pretty much all of the networks because of scalability solutions.

Example of Permissionless vs Permissioned

Credits by MarkTheShark of Hydro
Posted on Philippine Decentralized and Centralized Blockchain
Have a great day all!