SDC offers anonymous transactions in the form of zero knowledge interactive proofs coupled with ring signatures. The ShadowSendv2 whitepaper can be found here if you'd like more details.
http://shadow.cash/downloads/shadowcash-anon.pdfAs far as I know, the system is very similar to Monero's, although SDC is a little bit more user friendly. I don't believe Monero's system destroys and mints new coins though.
In short, when using ShadowSend, coins are destroyed for freshly minted tokens. The tokens can be held as token for however long the user wishes. The tokens basically grant proof of ownership for future, freshly minted coins at an exchange rate of 1:1. Proving ownership is done by the use of ring signatures.
And as far as I know, zero knowledge interactive proofs are the highest level of secure, transaction anonymity possible today. If a coin is able to integrate zk-SNARKS, then that coin would have the highest level of anonymity.