Liquid has hidden amounts which is good, but the addresses can still be linked.
If you want privacy (yes! don't use monero!) you should coin join or use an unannounced lightning channel.
Discussion
Why shouldn't he use Monero?
It's the best strong default privacy tool available right now if you want to transact p2p, non-custodially, and without permisson.
Using it doesn't mean you have to save with it.
Coinjoins have many problems. They are a weaker form of privacy via obfuscation everything is still visible (not truly hidden like Monero encrypted amounts and addresses). Largely require centralized coordinators so are vulnerable to censorship. Opt in active participation instead of being on by default. They are relatively expensive, slow, and tedious. And you can easily make mistakes that degrade your already weaker privacy.
Lightning is not private. Reciever privacy is particularly bad. You're still not private to anyone who sends to you even with unannounced channels. So many other issues Monero doesn't have...
-need capacity to even recieve to begin with
-limited in the amount you can send without failing
-can't transact without both parties being online at the time of transaction
-can be rugged if your node is offline
-can be force closed onto the base chain against your will
-ability to grief honest users with zero cost
-recent unresolvable critical security issues without base layer changes
lists.linuxfoundation.org/pipermail/lightning-dev/2023-October/004154.html
Monero can't verify their supply. Smaller group of people use monero so privacy isn't as good as you think.
Unannounced lightning channels are private.
Dude first off privacy is different from anonymity. Bitcoin is a public blockchain. All connections and amounts are visible to anyone in the world. Can't ever truly be private.
Second, do you think all of the Bitcoin network is your anonymity set? No, your anon set is the peers that actively particpate in your coinjoin rounds. Which is like what? 0.000000001% of users? Your psuedonymity is not as good as you think.
Unannounced lightning channels are not private from anyone you are interacting with that sends to you. Are you just never going to recieve ever?
" “We call private channels 'private' but they are really not, they are more like unannounced channels,” Giorgio said, adding that there are currently ways to exploit the Lightning Network that enable a node to discover an unannounced private channel."
https://bitcoinmagazine.com/technical/state-of-bitcoin-lightning-network-privacy
Even worse, no one does this anyway, 95% of lightning users are on custodial wallets like WoS (they can see everything). And the remaining are trusting Phoenix servers that aren't private either.
https://phoenix.acinq.co/faq#how-private-are-my-payments-on-phoenix
You rely on a node to verify Bitcoin supply just like Monero.
Don't pretend like you take advantage of Bitcoin's simple transparency to audit. Did you make sure every single transaction in 817,000+ blocks inputs = outputs? No, you didnt and niether does any Bitcoiner. You just rely on your node to verify supply for you like any Monero user.
There's literally no difference in practice.
Privacy on bitcoin is good enough if you know what you're doing. Unannounced LN channels have hops in between, there are trampoline routing too. You don't need to sh$tcoin.