Welcome to Secret.
Secret has no real competitors right now. There are some pre-launch coins trying to play catch up, but getting here has been a several year ordeal. The real competitors currently are probably SGX enabled cloud providers.
Secret, at the core, is not competing for private transactions, in the financial sense. Monero and ZCash already do a really good job at that, and are willing to sacrifice all sorts of other aspects to maximize transactional privacy.
What Secret brings are secret contracts. One can’t examine the state of a contract, it’s inputs, or it’s outputs. Secret is functionally most similar to Ethereum; We can support any kind of dapp you’d find there, from cryptokitties to ICOs to uniswap, but also do it privately.
The implication is that smart contracts on Secret could process a blood sample, run your taxes, or search your text messages, and you wouldn’t have to worry about the fact that the chain was transparent and permanent. It’s secret.
To address your question, It’s true - Tezos and many others are implementing Sapling or MimbleWImble. And Tezos in particular has applied Sapling to some aspects of its smart contracts. However it is an optional add-on feature that takes a backseat to the rest of the network. I look forward to exploring Edo more when it’s released, but as far as I know it’s strongly focused on zk-proof fund pools for doing private token interactions.
Token interactions are only a tiny facet of what’s possible on Secret, which supports fully private computation on any type of contract. Additionally, Tezo’s approach with Sapling privacy pools is more computationally complex and therefore difficult to integrate into a lightweight browser hotwallet like we have with Keplr. We want a vibrant ecosystem, filled with interactive web applications. And we want Secrecy to be a core design decision.
As for MimbleWimble - it’s a creative efficiency innovation with nice privacy implications. It’s great, but only moderately so for secrecy, without Dandelion, Tor, and other numerous privacy focused technologies layered in. It’s in an entirely different class of privacy tools compared to sMPC, SGX, or Sapling. I don’t consider it a competitor as far as the goals of Secret are concerned.