Metadata, IP addresses, and amounts are always the most important factors when it comes to privacy, so I wouldn't consider calling out problems relating to them as left curve.

Short Answer: The fact that Monero doesn't rely on trust to function is why it's more private over Cashu and BDHKE. XMR is trust less, Cashu is not.

Long Answer: Monero uses different technologies to conceal metadata, such as ring signatures and stealth addresses, preventing the re-use of addresses, whereas Cashu uses blind signatures and relies upon trust of the mint used.

XMR also uses Dandelion++, which is essentially it's own onion routing network, to protect IP addresses. You can also take it a step further and incorporate I2P into transactions through Kovri. While Cashu is received offline, the only problem that is that off-layer protections Cashu has do not apply to the entire Bitcoin blockchain, so once a transaction from Cashu is done and the sats go back to being on-chain, more privacy risks arise.

Finally, XMR conceals amounts using RingCT. Much like with metadata concerns, Cashu's privacy is also reliant upon custodians to keep it private by not log or timestamp activities. If a mint does logging, then correlations for activities could be made.