Examples of default transactions for each...

IP: ?
~6% chance Alice sent $[?] to [?]

IP: Alice
[?] sent $[?*] to Bob

* = discoverable

As you see, with lightning, your IP being exposed nullifies lightning's good sender privacy (You know based off IP that it was Alice who sent to Bob)

Even if you optionally hide your IP when using lightning with Tor or at least a VPN: The receiver remains distinctly visible (non-ambiguous) and potential to discover amounts is still there.

With Monero, the best an adversary has (all things equal) is a probabilistic  ambiguous sender (AKA guess work). (1 real sender, 15 decoys) ~6% chance of a ring member being the true sender and that chance falls off rapidly even after 1 hop = ~0.4%, 2 hops = ~0.02%, etc...
And unlike Lightning, amounts and recievers are completely hidden.