Zcash and Ethereum are not competition, they're complimentary. That is why Zcash on NEAR Intents is such a big deal. Near Intents connects Zcash to the rest of crypto.
Recently Richard Heart has noted that Ethereum is more private than Zcash, but it really depends on the use case. If you're using Zcash as a cash replacement, and not depositing it into a crypto bank (i.e. exchange), then Zcash is more private. But if you're doing more complex things that require you to connect Zcash to the outside world then you're privacy is naturally compromised. It's just like when you have cash, as soon as you deposit cash into a bank you lose the privacy of cash.
As Zcash is private at the base layer, it's inherently more private than Ethereum, which has privacy added on top of the base layer.
Saying that Ethereum is more private than Zcash is like saying that an economy car is better than a sports car. In the case for a person that's commuting an hour on rough roads, an economy car is definitely better. The economy car usually has softer suspension, an automatic transmission, and better gas mileage. So Ethereum, the economy car of finance; with it's smart contract capabilities and all in one solution, is better as a upgrade to the banking system, but it's not an upgrade to physical cash system.
As physical cash can be debased at anytime by the government, a system that's outside of the government's control is a big upgrade. Hence, Zcash, is a replacement for cash. Just as the privacy of cash is lost when you deposit it into a bank account, the privacy of Zcash is lost when you bridge to stablecoins. But just using Zcash as a cash replacement and not bridging out is the most private way to crypto.
Enjoy.