Monero badly leaks data it shouldn't (https://moneroleaks.xyz). LN is actually privacy for BTC from what I've been reading.
https://v.nostr.build/Ysnt7q02fO8TmDSB.mp4
Bitcoin is institutional grade.
Monero is freedom grade money for the people.
"I've been warning Bitcoin developers for ten years that privacy needs to be provided for at the protocol level. This is the final warning. The clock is ticking." - Edward Snowden

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LN leaks payment amounts to third party nodes along a route.
Monero completely hides the amount you're sending to your counter party from all nodes on the network - even if you're using someone elses node.
LN privacy sounds great in theory, but no one uses it like that, it's moot when 95% of users are on things like Strike or Wallet of Satoshi that can see everything their users are doing (because the bar to achieve good privacy on LN is higher than Monero)