According to a recent study, the privacy properties of the lighting Network are weak.

The problem with lightning privacy is that to get good privacy you need more than about 2 hops. The problem is that every hop locks up money equal to the amount transferred: increasing the cost of the transaction.

The study also finds that the LN is currently subsidized, and based on the capital costs alone, fees should be comparable to on-chain (BTC) transactions. BCH transactions are currently subsidized as well, but not to the same extent (I estimate 3cents/kB would pay for processing and storage).

https://blog.dshr.org/2020/01/bitcoins-lightning-network.htm...