Proof of Authority (PoA) means that the blocks are produced by known and trusted nodes. The DLT uses PoA for a number of reasons. Firstly, it makes sense for the block producers to be trusted internal nodes run by the customer. A cryptocurrency consensus protocol is all about who has control. A customer using DLT will want to know that they have control of the cryptocurrency they’re using. Private sidechains can be Proof of Work (PoW) and Proof of Stake (PoS).
Besides the need to incentivise good actors with PoW and PoS (see point 2.), PoA has a few characteristics which may be attractive to customers: it requires low computational power, doesn’t require communication between nodes to achieve consensus and block intervals can be predicted with 100% accuracy so long as it is known which nodes are online, something which is not possible with PoW or poS.
2) The private sidechains are pegged to the Stratis mainchain by pegging the coins of the sidechain to STRAT, meaning the sidechain coins will have value. By comparison, DLT coins won’t need to have value.
The sidechain coins have value because they pegged to STRAT. The value of the sidechain coin is pegged to the value of STRAT (you can read more about how, here). For that reason, there are applications which will suit private sidechains better than DLT. For example, any application which needs to service an economy as part of the application. This could be something like an internal payment reconciliation system.
The value consideration also plays into the consensus protocols of private sidechains and the DLT talked about in point 1. You need to incentivise node operators in order for PoW and PoS to work. The easiest way of doing this is by rewarding node operators with coins of the value-bearing currency. This is not a consideration with the DLT since PoA does not require the same incentivisation of good behaviour: why would the trusted node sabotage its own chain? Trusted nodes could either be a single, centralized node, in which case it is a good actor by definition, or it could be a group of nodes operated by the involved parties (like in the airport example given in What is the Stratis DLT?) in which case any bad actors would be identified.
A PoA cryptocurrency will always follow the longest chain. In the instance that private keys of nodes are compromised, so long as 51% of the nodes are honest or uncompromised, the longest chain will be the best chain. In this sense, PoA can retain the extra layer of security that comes with decentralisation, if that is a consideration for the application.