How does MWEB compare to LN in term of privacy?

I have had a conversation yesterday regarding MWEB. That man was saying that LN was more anonymous/private than MWEB. I told no but didnt have the technical arguments to actually prove him he was wrong
My only argument was that if @coblee worked on MWEB to add privacy after LN implementation on LTC there was for sure a logical reason

Can I have an explanation on how the both compare in terms of privacy? Is one stronger than the other? Can we add one of top of the other?

Tx in advance


I would appreciate if you could give more clarity onto the forum. This is what its made for