Fine left curve, but in monero you need to be an active adversary to guess the transaction broadcaster, in cashu the mint absent any proxy always knows. There is an asymmetry there.
I'd say Monero's current cryptography is weaker, though that might change soon.
The lack of a middleman definitely makes XMR slightly better cryptography wise. With Cashu, you literally have to place trust in the mint not to deanonymize you.
Cashu is trusted, XMR is trustless.
How do you, as a mint, deanonymize?
Even an account based mint only can know amount at a given moment.
I bring you a cashu proof, how do you know its origin?
From "out-of-bound" transactions and using larger denominations. Not to mention that Cashu does not have privacy at the network level, which means mints can trace users from logs and timestamps, which can be used to correlate things such as the user themselves or their location.
Again, this is all information that Cashu's own developers have warned about on their site. https://docs.cashu.space/faq
Talking anonymous and privately to an http server is a fairly solved problem. VPN + TOR is a good first step among many.
