Well, first off, 95% of LN users are on custodial wallets and LSPs that can see everything...so we can cross them out completely...
But even if everyone only ran and used their own LN nodes, receiver privacy sucks and hidden balances can be discovered by probing. Many other things involved like onchain data leaks when opening/closing channels.
It would be relatively easy for a big actor running a large LN node to get a good picture of most of the LN network and save all that data. The effectiveness of onion routing is reduced as LN centralizes over time by everyone routing thru large nodes. Governments, IRS, chain analysis, and even large nodes being coerced with a gag order have all the incentive in the world to do this.
With Monero, even if you don't use your own node you still get all the privacy benefits. A remote node doesn't know who the real spender is, and can't see amounts or receivers at all.
So I guess it just depends if you want kind-sorta-maybe privacy or actual privacy from third parties.